It's a chess showdown quite unlike any other: on one side, arguably the greatest player of all time, Garry Kasparov, former world champion and now Russian exile. On the other, Kirsan Ilyumzhinov, a Russian multimillionaire perhaps best known for his closeness to dictators such as Bashar al-Assad. That and his claim to have been abducted by aliens.

After officially registering earlier this week, the two are now facing off for the presidency of the World Chess Federation (Fide), which will be decided in August at the World Chess Olympiad in the Arctic city of Tromsø, Norway.

In many ways, the election will be a clash of epic proportions, a battle between a long-time president and a new challenger, between Russia and the West, between personal patronage and corporate sponsorship, between old friends turned enemies. But most of all it is a showdown between two of the most forceful personalities in the ego-filled world of professional chess.

"I believe in the cosmos. Buddha, Christ and Mohammad just came to this world to pass along teachings … I came to this world to help people," Ilyumzhinov said when asked why he is running for reelection in an interview in the Moscow office of his Russian Financial Alliance bank. His mission, he said, is to bring peace to the world through chess. To this end, he has pledged to raise the number of chess players from an estimated 600 million to 1 billion over the next five years.

"This billion people is a critical mass. Ministers and presidents will come from this mass, and before they issue an order they will think," he said, echoing his favourite chess mantra of thought before action. "Then wars will end and peace will start to come."

When Ilyumzhinov says he believes in the cosmos, he means it: The Fide president, who has been in office for 18 years, believes human civilization is a product not of god or evolution, but rather of extraterrestrial intervention. He insists aliens in yellow spacesuits abducted him from his Moscow apartment balcony in 1997. And he argues that the game of chess is a "certain code that another civilization gave us" and suggests that it could help man recover his lost abilities of flight and telepathy.

It is such less-than-mainstream beliefs that Ilyumzhinov's critics see as a liability for Fide. Kasparov called his statements on extraterrestrials a "disaster for the organisation" and a hindrance to its growth. Ilyumzhinov's image has been suffering over the eagerly anticipated World Chess Championship match in November between record-breaking prodigy Magnus Carlsen and former reigning champion Viswanathan Anand, which still doesn't have a sponsor or a venue after a deadline for bids recently passed.

"No western sponsor will ever be with someone who talks about aliens and visits all the worse dictatorships in the world," Kasparov told the Guardian by phone from his latest campaign stop in Oslo. The grandmaster left Russia last year over fears of political prosecution after years of opposition politics and police detentions. He was granted Croatian citizenship in February, choosing the country because it allowed him to keep his Russian passport, he said.

The mudslinging campaign is already in full swing, with both sides tarnished by scandal this year. A leaked memo showed that Ilyumzhinov and Andrew Paulson, a London-based entrepreneur who founded several popular Russian media outlets, had planned to create a company to hold chess events, splitting the profits.

Another leaked document revealed what appeared to be a vote-buying scheme between Kasparov and Fide general secretary Ignatius Leong. Both denied the claims. Kasparov later posted a copy of a final contract with Leong on his website, while Ilyumzhinov said his deal with Paulson was never approved.

Ilyumzhinov denies Fide has had problems attracting sponsors, arguing that $5.5m (£3m) was raised for the last world championship. He said three countries have expressed interest in hosting the Anand-Carlsen match, but if all else fails he will contribute the cash himself. Over the years, he's spent up to $80m of his own money on chess, he said, including $1.5m to sponsor the 2003 match between Kasparov and the chess program Deep Junior, which ended in a tie.

As for rubbing shoulders with dictators, Ilyumzhinov does have a talent for turning up in countries most public figures have long since forsaken. He famously played a friendly game of chess with Muammar Gaddafi in Tripoli during the Nato bombing campaign in 2011 and visited Saddam Hussein shortly before the US invasion in 2003. More recently, he met with Assad in Damascus in 2012 to discuss Ilyumzhinov's beloved chess in schools programme.

As the president of Russia's Kalmykia republic from 1993 to 2010, Ilyumzhinov undoubtedly has close ties to the Kremlin, and a woven rug featuring Putin's face hangs in his office. Arkady Dvorkovich, an aide to then-president Dmitry Medvedev, sent armed men to the Russian Chess Federation office when that organisation briefly backed grandmaster Anatoly Karpov against Ilyumzhinov for Fide president in 2010. And tellingly, the last large investment Fide secured was $1m for the chess in schools programme from Russian state-owned oil company Rosneft.

The Fide website reported this week that 56 national federations have endorsed Ilyumzhinov, whereas only 20 have endorsed Kasparov. But according to British grandmaster Nigel Short, who supports Kasparov as the man to solve Fide's "credibility problem," the race will be very close.

"It certainly will not be like in 2010 or 2006 when Ilyumzhinov beat off the challengers pretty convincingly," he said.