Arjen Robben is a machine. He might, in the past, have been a highly calibrated unit with a tendency to occasionally malfunction at the worst possible moment. But put aside, if you can, the debate over his theatrics against Mexico in the second round and – before his personal semi-final duel with Lionel Messi – he has a strong claim to be the player of the tournament so far.

At this World Cup he has resembled nothing so much as the T-1000, the robotic bad guy in the second of Terminator films. After every tumble, twist and fall he has got back up again and resumed his fast, direct running at the defence – head up, ball at his feet and panic in the eyes of his prey.

While so much of the attention has, perhaps by design, been on the manager Louis van Gaal’s tactics and tics, it is Robben who has powered the side to the semi-finals.

The statistics – three man of the match awards, three goals, one assist and that last-minute penalty against Mexico that highlighted the best and worst of his game (it was both a foul and a dive) – don’t tell the whole story. From Holland’s first game, that 5-1 evisceration of Spain that signalled not only the end of an era but also sent confidence coursing through Oranje veins, to their nervy, attritional victory over Costa Rica on penalties, he has been Van Gaal’s one constant.

You will not see his face staring down from many billboards in Brazil, nor does he feature on the back of many replica shirts. Yet while the poster boys – Neymar, Wayne Rooney, Cristiano Ronaldo, James Rodríguez – have one by one fallen by the wayside for a range of reasons, Robben has relentlessly kept going. Only he and Messi remain.

Aged 30, this is his sixth major tournament. But while he has gone into others ill at ease or carrying injuries, here he has looked determined to seize his moment. Empowered by Van Gaal’s trust – he is the only player indulged with his own training routine and is absolved of defensive responsibilities – he has revelled in his role as one of the leaders of the team.

How much of that drive is down to the memory of the chance he missed in the 2010 final against Spain, when clean through with only Iker Casillas to beat, is one for the amateur psychologists but it must surely be a factor.

In the Costa Rica quarter-final, where Holland disappointed for long periods despite their dominance of possession and territory, he was the player who kept them going.

Before the game the Costa Rica coach, Jorge Luis Pinto, had made pointed reference to Robben’s diving against Mexico. Afterwards, the midfielder Celso Borges admitted the plan was to have at least two players marking him at all times. It made no difference. Popping up on the left, the right or through the middle he was a constant menace to the massed Costa Rica defence.

He also appeared to have decided to stay on his feet if possible. A string of players were booked for fouls on Robben and one, Júnior Díaz, should have been sent off. The Dutchman has no one to blame but himself for his reputation as a diver but the furore over when and how Robben goes to ground has threatened to overshadow appreciation of his genius.

After celebrating on the pitch in Salvador with his son Luka, he let his frustration show. “In recent days there has been a lot of talk about diving and actually I’m tired of this bullshit,” he told the Dutch broadcaster NOS. “I get kicked from all sides but luckily I am still fit.”

Robben has maintained the speed and skill of his youth but added experience and physicality. Where he might previously have chosen the wrong option, he will now – with a dip of the shoulder or a clever through ball – make space for others. He has certainly lost none of his confidence. “I felt that I could make the difference but didn’t get the ball enough. I don’t want to blow my own trumpet but I felt I was so good,” he said after the quarter-final.

And when the Costa Rica match went to extra time, it was a sweat-drenched Robben doing the rounds of his younger team-mates to cajole and inspire them. Similarly against Mexico, Van Gaal said it had been Robben who used the water break to inspire his side to overhaul a one-goal deficit. When they restarted, he played like a man possessed.

Bert Van Marwijk, the Dutch coach in 2010, has admitted he is a “little bit jealous” at how well Robben is playing this time round. “Four years ago, Arjen was injured just before the start of the tournament in a friendly against Hungary,” he told NOS. “He was carrying the injury for the whole tournament and was never really 100%. But this year he’s been unstoppable.”

For all Robben’s injury problems down the years, and his apologists will point to his fitness concerns as a key reason why he often takes evasive action, he has huge experience to draw on. In the last two years at Bayern Munich he has looked a different player from the callow, fragile winger who terrorised defences and infuriated José Mourinho in equal measure during his time in England.

Just as Messi will carry Argentina’s hopes into Wednesday night’s semi-final in São Paulo, so Holland’s are increasingly pinned on Robben.

The strain of recovering from injury in time to lead his side in Brazil is starting to show in Van Persie’s legs and for all Van Gaal’s tactical genius, this Holland side remain a fragile marriage of a handful of big-game players and willing but inexperienced youth.

Under leaden Sao Paulo skies Robben trained at the historic Pacaembu stadium in the centre of the city on Tuesday with a Dutch squad who are fuelled by a growing belief they have destiny on their side. “Argentina have got Messi, we’ve got Robben. And quite frankly, I think the better player is Arjen,” said Van Marwijk.

If they are to beat Argentina at the Arena Corinithans and give themselves another chance to banish the ghosts of three lost World Cup finals, Robben will again need to be firing on all cylinders. If he does, he may even get the recognition he deserves.