My girlfriend ignores me and just plays on her phone.
Do you think that's a good-enough reason to break up with her?
Yes, I've asked her many times to play with me instead.
It's okay if your partner wants to play games on her phone, but she shouldn't be playing them to excess.  If you feel that you are being neglected in your relationship, and if you have already told her how you feel, then you might be better off breaking up.
I'm going to break up with her since she liked the games more than me.
Fair enough. People don't want to be neglected.