You can paint paneling. It might be fun to have some darkish walls down there for the gaming center - something like Sherwin Williams Naval? I sort of like the carpet, but it does read Granny chic. Probably you should replace it with something a little less colorful - maybe a silvery gray if you do the navy walls. Leave the ceiling because no one cares.

I think the paneling is kind of fun, especially if you’re going for a cozy environment. I’d for sure replace the carpet, though. It’s not any kind of chic. Your ceiling tiles may be asbestos - removing them will cost a bundle. I believe you can paint them, though. Please consult an expert on the ceiling.

The ceiling is probably fiberboard tiles attached with staples to wood furring which is nailed to the floor joists. The joints lap to cover the staples, making it difficult to remove individual tiles. Unless, you want a large project you may want to leave it alone. I doubt it contains asbestos but you never know.

You may want to look at new lighting. You could leave the lights that are there or try and upgrade, but I might not use them, and instead get some up lights to bounce light off the ceiling. It will be a much softer effect and less glare for gaming.

Peel a little of that carpet up and see if there's some kind of vinyl tile underneath.

Decide how you're going to use the room first. Home theaters, in particular, have different requirements than other types of rooms. For example, you might paint the ceiling dark for a home theater but white (to cover the dirty and mis-matching tiles) for another use.

If you play with others online, then you really want to put up a wall so no one hears you.