A very small percentage of your carbon footprint comes from playing video games. The majority of domestic electricity use is from heating/air conditioning, water heating, major appliances (mainly your fridge and clothes drying), and lighting. TVs and all related peripherals (e.g., game consoles, cable/satellite boxes, DVD/Blu-ray players) combined average about 7% of all electricity usage. (Source: U.S. Energy Information Administration).
Even if everybody stopped playing video games, it wouldn't make a dent on our combined CO2 emissions. Keeping the temperature comfortable in your house produces far more CO2, so see if alternate means of climate control are viable for you. Driving produces more CO2, so reduce your trips, ride with other people, or walk/bike when you can. And this would all be a non-issue anyway if we transitioned away from fossil fuels for electricity generation. Instead of ditching our hobbies, we'd make more of an impact if we ditched coal and gas for nuclear and renewables for electricity generaiton (residential solar needs to be a lot cheaper), and transitioned from gasoline-powered vehicles to electric vehicles for transportation.
As for the garbage gaming produces, I've done the math, and games don't produce that much garbage. On the software side, as of Dec. 31, 2019, there were just over 1.1 billion PS4 games shipped globally. Now, presumably not all of those are physical copies, but let's assume that about 80% of them are, meaning nearly 900 million discs. One PS4 disc has the standard DVD/BD volume of about 13.57 cubic centimeters, so if you melted all those discs down and made a cube out of them said cube would be only a little over 23 meters per edge. That could fit into my small-ish back yard, and would only be a tiny section of the typical landfill. And the game cases (original dimensions, meaning not melted down, since they are storage boxes) occupy only about 23.67 times the volume of a disc, meaning a roughly cubic shaped stack of 900 million PS4 game cases would be about 66 meters per edge. So, even if every PS4 owner in the world threw out all of their physical copies, case and all, the amount of garbage would be far, far from ruinous (in the U.S. alone, all the garbage tossed in one year amounts to a cube 805 meters tall), and I'd submit that only a tiny percentage of those games actually will be discarded. Oh, and game discs and cases can be recycled.
TL;DR, you don't need to feel guilty for playing video games, any more than you need to feel guilty for enjoying the occasional hamburger. The impact is minimal compared to other things we do.