The 5570 is a good multimedia card, but won't give you good gaming performance. If you don't mind setting the graphics to low, you could probably play most games beyond 30 fps. The fact that it has 2GB would seem to not matter unless your were to drive additional monitors with it (kind of defeating the purpose of the all-in-one) or if the monitor had a resolution beyond 1080p.
The 5570 is a bit better than the 425m according to this performance chart:http://www.videocardbenchmark.net/high_end_gpus.html
That machine should be great for everything other than gaming. For gaming, you'll need to set everything to low.