Considering many games make use of cloud computing for online play and similar functions, they probably make up a pretty goot bit of global cloud compute capacity. Likely quite a lot less than the big AI players, but not an insignificant amount.
The energy costs of the cloud computing required for gaming are substantially less in power - not to mention overall demand - than LLMs. Come on, we're not in the same energy ballpark here.
You're not including the physical supply chain energy consumption of distributing video game equipment in this analysis. Nobody ships LLMs to big box stores and tries to sell them to consumers.