I'm going to play videogames with a girl when my gf hates her and has told me not to
What do you mean?
Oh believe me, I am confused on how to act on this.
While you are free to hang out with whomever you want, you still have to be considerate to your significant other. You have to choose between the two of them, do you want to hurt your girlfriend more or have fun with another girl?
Of course I don't want to hurt her but I also want to relax and I think my girl friend hated the idea of me having fun with the other girl.
I think that if she has asked you to not play with this girl, then you should listen to that. It is not okay to do things that are just going to hurt your significant other.