For basic windows tasks even an IGP is fine. HD4000 can run 2560x1440 just fine with no issues and no lag at all. So to the first question, yes, the 7770 is actually more than you need for 2D windows.
Now when you say "little gaming" that's a somewhat vague statement, the 7770 isn't a gaming powerhouse obviously, so it really depends on what games you have in mind. You can play undemanding games. Stuff like Diablo 3 on low/medium? Sure. Legend of Grimrock? Yeah. Don't expect to run any AAA titles without either significant compromises or lowering the resolution, though. You're not going to run crysis 3 or metro LL anywhere near decent settings at 25x14 with a 7770. I actually would expect a 7770 to chug in those games without lowering the resolution a bit. So, to answer the gaming question, that entirely depends on what games you want to play.