Unlikely, but possible - given the right conditions
War exists because it is a real threat. It destroys resources and kills people, and does not rely on an honor system to function. If a country no longer has the ability to fight back, it no longer has a say in arguments. Countries with military forces will not capitulate because they lost a game, if they have the ability to win a real war afterwards.
But war is terrible for everyone involved. Even the winners lose out on a lot - if they could get what they want without fighting, they would. The interest in resolving conflicts before they start has driven both society and evolution to create alternate means of competition; countless forms of posturing and non-lethal combat are found across the animal kingdom and human societies.
The higher the cost of injury, the more likely non-physical forms of competition are to occur. Birds love non-physical confrontations because it is very, very easy for a bird to suffer an injury that will leave it unable to fly and vulnerable to predators - even if it wins the fight. There are island tribes that do not engage in physical warfare because their populations and territories are so small that a full confrontation could easily wipe them out entirely. And with the threat of mutually assured destruction, modern civilizations may be in a similar situation as well.
However, what all of them have in common is that the ability to win the competition must indicate the ability to win a real fight. Animals posture by showing off their large horns, wrestling or throwing things around to show off their strength, singing or stotting to demonstrate their abundant energy. The loser of the confrontation backs down because it realizes it will lose if the conflict actually escalates to physical fighting.
If war is to be replaced by games, those games must accurately represent the players' ability to win a real war. A sufficiently accurate VR sim may work, but the competition will not be "fair" - countries will receive in-game resources reflecting their real-life resources. The game must be designed in a way that, if a country loses, that loss will be definitive enough that the country's leaders will not try to turn the in-game war into a real-life one.
The more costly the threat of war becomes (especially if the war is likely to be costly to the winner), the more likely such a system is to work. Right now, nuclear-armed countries generally do not attack each other directly, instead opting to fund armies by proxy in poorer countries - which is pretty much like playing a game, in a way, although it is a game where other people die. A game-based means of conflict resolution may indeed be in our future, but only time will tell.