##Just explain you need "me time"

I work a concentration intensive job and I'm introvert-ish regarding how I relax. I need to zone out every once in a while, gaming is a perfect outlet. I do like it if my girlfriend is in the same room, I mind getting distracted.

You can make it her choice:

Hey X.
I use our off days to relax a bit, a little me-time, gaming helps me do that, so that when you're around I can do fun activities. I like the not having to talk to anyone or interact with anyone part of it, which isn't anything personal, I just need that sometimes.

I like it when you're around, so if you want to read a book or anything, that would be fine, but I'm not going to be very talkative.

##Just explain you need "me time"

I work a concentration intensive job and I'm introvert-ish regarding how I relax. I need to zone out every once in a while, gaming is a perfect outlet. I like it if my girlfriend is in the same room, I just mind getting distracted/disturbed.

You can make it her choice:

Hey X.
I use our off days to relax a bit, a little me-time, gaming helps me do that, so that when you're around I can do fun activities. I like the not having to talk to anyone or interact with anyone part of it, which isn't anything personal, I just need that sometimes.

I do like it when you're around, so if you want to read a book or something, that would be fine, but I'm not going to be very talkative. It's up to you.

When she comes over, stick to that. If she keeps disdurbing you, just explain it again. If everything if fine, don't forget to "reward" that. You could after, say an hour, drink a cup of tea together. Or maybe watch a episode of something.