I've been in that kind of rut before. The only way I can get out of it, is to make changes to a routine that's become toxic. You said it yourself

I feel guilty playing games when I'm meant to be studying, but I'm not studying either so I'm in an endless cycle of no productivity and no fun.

You're instinctively punishing yourself mentally in order to get yourself back on track where you can feel you're doing something worthwhile. Maybe you take a serious look at whether you could do better in gaming, than what you are studying for? There are gamers that became millionaires through gaming. Are you that caliber of gamer?

I'd say you're at a crossroads for making a decision on what you want to do with your life, or becoming victim to the risk of falling further into that endless cycle you mentioned. Whichever one it is, you need to make some decisions.