GPU:
AMD Radeon 7610MIt's an entry-level, low power gaming card, but it *should* be able to handle something like the game you're trying to play... APB-R didn't look extremely graphics intensive by any means at first glance.
DDR3 RAM is good for gaming, although again, 4Gb is pretty shy, which we already know.
CPU:
Intel Pentium B960 clocked at 2.2 GHzNot bad, doesn't compete with a Core i-series, but it should work fine for moderate intensity games, I don't see any issues with the game you're trying to play.
My guess would be that RAM is your biggest bottleneck for the moment... some laptops have upgradable RAM, so that may be an option.
A
demonstration on how a RAM upgrade is performed.