Although this was published in 2003 it appears to match most of what you describe. It is the fourth book in the Alex Rider series and unsurprisingly the main character is fourteen year old Alex Rider.
Sir Damian Cray is a philanthropist, peace activist, and the world's most famous pop star. But still it's not enough. He needs more if he is to save the world. Trouble is, only Alex Rider recognizes that it's the world that needs saving from Sir Damian Cray. Underneath the luster of glamour and fame lies a twisted mind, ready to sacrifice the world for his beliefs. But in the past, Alex has always had the backing of the government. This time, he's on his own. Can one teenager convince the world that the most popular man on earth is a madman bent on destruction-before time runs out?
His father was killed before the first book but the antagonist is Sir Damian Cray who is selling a new video game: Feathered Serpent. Alex initially plays the game at it's unveiling in front of a live crowd and is later captured by Cray and forced to play through a real version of it.
Failing to convince MI6, Alex starts his own investigations on Cray and attends Cray's launch of a new game Feathered Serpent, in which he participates in a demonstration. His suspicions about Cray grow as the next day Alex hears about the death of a journalist who was questioning Cray over the violence of the game. He then locates a journalist named Marc Antonio, a friend of Edward Pleasure, in Paris, who was investigating Cray. Marc reveals what he has been investigating Cray and a deal he made with a man called Charlie Ropper, an American NSA agent. Marc is killed by Cray's men, while Alex manages to escape. Alex sneaks into Cray Software Technologies in Amsterdam, where he hears Ropper and Cray talking about a flash drive, before they start arguing about the deal. Ropper is then trapped in a room, and two million dollars worth of nickels (owed to him by Cray as part of their deal) is poured on top of him, both paying and killing him. Cray catches Alex as he tries to sneak away and puts him in a real-life version of Feathered Serpent. Alex manages to escape and steals Cray's flash drive. A pursuit breaks out between Alex and Cray's men across the streets of Amsterdam, which Alex narrowly survives. In response to Alex stealing the flash drive, Cray captures Sabina and holds her for ransom. Alex attempts to force Cray to release Sabina, but Cray outmaneuvers him and forces Alex to hand over the flash drive. Cray then explains his reasons for attempting to have Sabina's father killed and having Antonio killed.
Wikipedia, Eagle Strike
Whilst I can't remember any crocodiles/alligators one of the Gods in the Mirror zone of the game is part alligator.
He had summoned three of them to patrol the mirror maze, the fifth and last zone in the huge arena he had built beneath the compound. Tlaloc, the god of rain, was half human, half alligator, with jagged teeth, claw-like hands and a thick scaly tail that dragged behind him. Xipe Totec, the lord of spring, had torn out his own eyes. They were still dangling in front of his gruesome, pain-distorted face. And Xolotl, bringer of fire, walked on feet that had been smashed and wrenched round to face backwards. Flames leapt out of his hands, reflected a hundred times in the mirrors and adding to the twisting clouds of smoke.
Eagle Strike, The Truth About Alex
The cover is indeed quite flashy: