When you get down to it, there's nothing "environmentally friendly" about video games at all. It's a leisure activity which consumes a lot of valuable commodities (electronics, plastics, electricity) without providing any real-world tangible benefit, and it's a leisure activity that only an extremely resource-rich society would even be able to consider let create a massive industry around.

An honest ESG score would factor in "do you actually need this thing to survive?", but that wouldn't produce the "right" result since when it comes down to it "bad" things like coal, oil, and industrial agriculture are far more critical to survival than video games.