If you have the money, and a bit of luck to avoid tornadoes and that type of shit, climate change won't really do much to you personally, speaking in the short-term. People most likely to be fucked in the near-term: poor people, coastal-dwelling people without the means to migrate, and uninformed/uneducated persons that cannot adjust to increased food prices, shifting temperatures, and so forth.
I'm not advocating for ignoring climate change, I just feel that upper-middle class and beyond won't really have major issues as the weather becomes more topsy-turvy. Sure, they'll hate the brutal cold winters and the sweltering summers as well, but that won't kill them like it'll kill poor people that lack the means to adjust.
How much blame does the gaming community get for global climate change? How much energy consumption and waste is the direct result of physical hardware purchased and disposed of by every person on the planet who plays video games? Since we're all concerned about the earth how much would it help if we all stopped buying and playing video games? Think of the savings on electricity and toxic waste from batteries and computer components that rot in the world's landfills.
Same can be said for television users, automobile purchasers, and people that work at restaurants and throw away extra food at the end of the night. I doubt video gamers contribute anywhere near as much as those categories, but your point still stands that yes, people that buy new hardware every 3/6/12/24 months are generally being inefficient from a resource standpoint. Ideally, every consumable product on Earth would only be replaced when the prior product breaks, or when the new one comes out and is drastically more energy efficient to the point that it makes sense on a carbon basis to recycle the old, working product to replace it with the newer, more efficient product.