Some really good points and advice here. I just want to add: you're 22. What you are experiencing is totally normal. Everyone goes through this struggle at some point in their lives - not necessarily with video games, it can be with other things. The guilt is a perfectly normal reaction to the situation, so no need to beat yourself up about it. What you are feeling are two opposing needs that need to be met - both are perfectly valid. The need to feel productive, and the need to feel relaxed. You need to acknowledge both.
Also, I am guessing that that need to feel productive may come from an expectation to achieve and possibly appear successful. If it is, it would be beneficial to really deeply question the motivation behind it. A lot of people at that age (including me, when I was) believe that you have to 'be' somebody. That is an external expectation that you would need to see through and let go of.
I always have trouble finding the real motivation and reasons behind things. I just don't what is the real questions I should be asking myself. For me, finding the why in things is sometimes really difficult. For instance, about exercising: I know that I should exercise so I'm healthier and live longer, but that reason alone sometimes isn't enough for me to get up in the morning and go for the jog. I guess I have a hard time acknowledging the fact that I need to relax sometimes, it's just that I don't really know any other form of relaxation but video games, and that makes me sad.
That's OK. Sometimes it takes time to find the real motivation behind something. Sometimes it doesn't make sense either, and that's OK, because it doesn't have to make sense, despite your mind thinking that it should. It takes an honesty with yourself to acknowledge those motivations as well. The key is to not beat yourself up about it too much. The more you do that, the more resistance you will feel about it.
Also, I am guessing that that need to feel productive may come from an expectation to achieve and possibly appear successful. If it is, it would be beneficial to really deeply question the motivation behind it. A lot of people at that age (including me, when I was) believe that you have to 'be' somebody. That is an external expectation that you would need to see through and let go of.