There is almost no affiliate network that is specially built for video games. However, you can search for games to promote on famous affiliate networks. One of the best network out there is Click Bank Marketplace. It is one of the biggest affiliate networks out there. It has a lot of products in different categories to be promoted by publishers. There are software and even video games in their huge directory. You can select a lot of products related to video games from there.
Here, I did a simple online research and Found this.
There commision is based on two tier, 1st tier with big commission and 2nd tier affiliates with good commission.
You can also join CPA networks that pays for video games sign ups or Installs.
Check offervault for best CPA network.
As the above user said, CB is also the best place to find and join the game affiliates.
have you considered marketing video games that are available on Amazon. You can earn a good sales commissions. However, the question is how are you going to market the products. Are you simply promoting on social media are building contents around a particular games and linking the content to the product. I thing good way to make sales is by reviewing the product and sharing affiliate link.
I suggest you try G2A Goldmine (Google it). They have an affiliate program where you can get commissions for every game you sell. You can also try Amazon if you want to. They are selling games as well. Right now I am experimenting them, since I'm experimenting something on autopilot. I believe they are a great affiliate program exclusive for video games. I hope my suggestion helps you. Cheers!