Yes, you can play games just fine with them. As to how they all compare? I'd say under ideal circumstances you'd have a difficult time telling an internal card apart from an external one. I've been a lot happier with my fiio because unlike every creative soundcard I've ever owned, I don't need to worry about searching for the magic driver version that won't hiss at me, not to mention the tendency of internal cards to suffer from audible interference due to all the other electrical components they are near.
All this being said, it is very silly to spend $220 for an audio source that you plan on plugging $150 headphones into. You'd quite honestly be better off investing that money in decent speakers, or even saving a bit and stepping up to nicer headphones with a cheaper dac like the fiio.