First, try to understand what's actually being said here. Sometimes I call myself fat because I'm above my target weight. But in my case my self-esteem is just fine: I'm a former gym rat who knows where I am, what I need to do to get back in shape, and that I'm still okay if I don't get there. Saying "I'm fat" is a light jab at myself and a reminder to take steps toward my goals, nothing to worry about.
If your GF is calling herself fat more hurtfully (which is sadly common) the issue is not how fat she is or isn't. That's just a symptom. The issue is whatever negative feeling is prompting her to tear herself down. Arguing with her about whether she's actually fat won't help with that, and might even do more harm than good. Maybe ask her how she's doing, remind her that you love her just the way she is.
Great video! I loved how, since the game has no choice acting, OneShortEye got a bunch of his friends to provide voice work for his game clips. Really makes it a more entertaining watch!