For the cynically minded it puts a new spin on the old Mrs Merton gag. So, captains of the global sports industry, what first attracted you to the tiny oil-rich state of Qatar?

The capital, Doha, is a city of contrasts. Queues of SUVs sit gridlocked on newly built highways even as it promises to invest billions in green technology. They carry Qataris with the highest per capita earnings in the world past immigrant workers whose treatment is concerning human rights groups and fuelling a huge construction boom that is poised to accelerate towards the 2022 World Cup. It has styled itself as the most modern and progressive of the Gulf states, yet faces a struggle to forge a new identity.

Twenty minutes' drive from the capital, past endless construction sites, one can view a scale model of a whole city, Lusail, that is yet to be built and by the time of the 2022 World Cup will be home to 400,000. The government-owned company behind it, Qatari Diar, already owns the London Shard, Chelsea Barracks and the Athletes' Village at London's Olympic Park. Stop on a busy nearby roundabout and one can gaze across the sand to the point where the stadium due to host the World Cup final in less than a decade in front of 86,250 fans will stand.

Construction of the 12 stadiums required, nine of them brand new, will begin in 2014 or 2015. "The heavy lifting is not the stadiums; it is the rest of the infrastructure. I don't see it as a challenge – I see it as a significant amount of work," says Hassan al-Thawadi, the secretary general of the Qatar 2022 supreme committee from his 37th floor office amid the towers of the West Bay district.

Two years on from Fifa's jaw-dropping decision to award the 2022 World Cup to a country where the furthest distance between stadiums is 70km and the temperature hits 41 degrees in the summer months, some of the cast involved on that heady day in Zürich were among those invited to the modestly titled Gathering Of All Leaders in Sport (Goals) conference in Doha. Part of an attempt to sell the strategy beneath the bling, as Qatar continues to engage in a trolley dash around world sport while simultaneously investing billions in building sports palaces at home, the two-day event was designed to demonstrate the social and economic value of its vision.

While much of the words from stage were platitudes, the hosting of an event that has pretensions to be the sporting equivalent of the Davos World Economic Forum was a statement in itself. As with the recent climate conference and its position as a go-between in delicate political negotiations, it is also part of an attempt to position Qatar as the diplomatic hub of the region. On the orders of the Emir, al-Jazeera broadcast live from the conference, while his paen to the development and educational potential of sport was on the front of every newspaper the next day.

Two of the men tightly woven into the narrative of this emirate's attempt to vault on to the world stage and position itself for a future without oil and gas were among those giving the opening speeches. Nicolas Sarkozy, the former French president at the centre of rumours (strenuously denied) that he encouraged the Uefa president, Michel Platini, to vote for Qatar due to France's important trade links with the country, was there. So, too, was the Fifa president Sepp Blatter, who did not vote for Qatar in Zurich but now has to make the great gamble work.

As Sarkozy claimed that Qatar sat at the nexus of many of the global challenges of the 21st century, Blatter again acclaimed the shift in the pendulum of sport away from the old European and American order. "There are big opportunities here, elevating ones presence in terms of seats at global tables and external image, but there are also risks. I would cite the Delhi 2010 Commonwealth Games," said Harvard professor Stephen Greyser from the platform.

The World Cup is just for starters. Doha twice failed at the shortlisting stage with recent bids to host the summer Olympics. Most recently, the International Olympic Committee sprung a surprise by agreeing to a proposal to stage the Games later than usual before dropping Doha from the shortlist anyway following lobbying by TV companies over scheduling concerns. It will try again for 2024. Meanwhile members of the Royal Family or state investment arms have bought Paris St-Germain and Málaga and deepened links with Barcelona that led first to Qatar Foundation and (from next season) Qatar Air being emblazoned on the front of previously unadorned shirts.

Like South Africa, Brazil and indeed London, Qatar has embraced the idea that hosting major sporting events can turbocharge and give a focal point to infrastructure development – except that in Qatar the figures are bigger and the stakes higher. "Qatar has a firm conviction about the importance of sport in stimulating various types of development that has led them to invest in building huge structures and sports facilities," said Emir Sheikh bin Khalifa al-Thani, opening the conference. He said it was "an important element in the development drive, knowledge building and job creation, not only at a local level but due to its benefits at the regional level".

It will spend up to £31bn on hotels, leisure, tourism, sports, recreation and other projects in the run-up to the World Cup. Reliable sources put the total figure to be invested in infrastructure over the next decade at £137bn. An entire rail network, a metro system, a new network of roads and that new city north of Doha are to be constructed over the next eight years.

Lord Coe, still on his London 2012 victory lap, met with the Emir, al-Thawadi and others involved in the Qatar's grand experiment to pass on his London experiences and bang the drum for British business. "They have genuine motives," said Coe. "It is easy to look at what you see here, the access to resources they have and the infrastructure they have. But they have looked at this and if you speak to the Emir he will tell you why they do it. It's about nation building, he sees sport as a means to inspire young people in his country and he looks at sport as something that introduces a completely different dimension. This is not year zero. It might appear like that to a lot of people."

The Qataris do not suffer from self-doubt. That new stadium is called, without irony, the Lusail Iconic Stadium. The pace of construction is breathtaking, endlessly accelerating over the past decade.

Showing off the indoor sporting facilities beneath the Aspire Dome, and on the endless manicured football pitches outside, they explain how they run programmes to train aspiring players from African nations and their own Qatari hopefuls. They outline the school programmes that hope to find Olympic medallists and they claim that the country, despite its relative youth, has a deep love of sport and is progressing quickly on the international stage.

But by vaulting on to that stage Qatar has invited scrutiny and suspicion. It likes to project itself as one of the most moderate and progressive nations in the region. But human rights groups have warned of issues surrounding low pay, poor conditions in labour camps and the fall-out from a sponsorship system that ties migrant workers to their employers. Al-Thawadi, left, says that the World Cup, far from exacerbating the problem, will act as an agent for change. "The World Cup is a catalyst. It will be addressed. We're making that commitment," he told the Guardian.

Qatar's successful World Cup campaign also sparked fevered speculation about the manner in which it was secured. All allegations of bribery and votes being linked to trade deals have been strenuously and repeatedly denied by the bidding team. But it is not in doubt that the Qataris spent unprecedented sums on a campaign that was bound by ill-focused rules with so many grey areas they were next to useless.

Al-Thawadi, who leads a fast growing multinational team, insists that he can't go on fighting battles of the past. There was bemusement from the Qataris at the allegations that came their way, claiming they stayed within the rules, had to spend big to announce their presence and put the most barbed allegations down to a disaffected ex-employee.

There are other things money alone will not solve. Qatar won the World Cup on the basis that it would be able to deal with the searing summer heat through innovative air-cooled stadiums but doubts have been cast on whether they will work on a large scale. Meanwhile a campaign started by Platini and stoked this week by Sarkozy for the tournament to move to winter, vigorously opposed by the European leagues, continues to gather pace. The Qatar 2022 organisers have consistently said they bid on the basis of hosting a summer tournament and are proceeding on that basis, but will move it if Fifa asks them to.

Ask how investments in PSG and Málaga and regular rumours about buying English clubs fit into Qatar's vision and al-Thawadi says it is a mistake to believe that there is an over-arching plan. "Everything has different pieces and everyone has different goals. In the end some things are interconnected and other things aren't. It's a complicated map. Some aspects are holistic and fit the national vision. Others are private initiatives," he says, sidestepping the fact that the line between state investment and individual initiative is inevitably blurred in a feudal monarchy.

Standing in front of a huge wall displaying a flurry of plans and diagrams headed "Programme Wide Masterplan: Stage One Draft", al-Thawadi talks a good game. He paints a picture of a compact tournament that will allow fans from across the world to experience a new kind of World Cup. Then you remember the taxi drivers who say it is impossible to go outside in July.

Three days in this fast-growing, disorienting city go some way to convincing that the deep-pocketed Qataris might just pull off the mission impossible of building the infrastructure to host a World Cup in oppressive heat from scratch. Whether it should have ever been there in the first place is a question that will not go away until the first visitors step into their cooled "fan zones".

Owen Gibson's trip was paid for by the Doha Goals conference