Interesting. :o By the looks of it, the Intel graphics chip did not allocate any extra memory despite the fact that you're running a game. Total physical memory stayed the same! This means either that tool is not a reliable way to measure memory allocation of that graphics chip, or the graphics chip doesn't work properly with that game at all. This would also explain the almost constant 100% CPU usage.
On the other hand, you can see that total memory usage, including the virtual RAM, doubled to about 1GB... even though you have only 512MB physical RAM. As such, it has to do time-expensive swapping every once in a while.
Based on this, the best guess I can make is that you should just get the graphics card. It should relieve the CPU of quite a bit of work. You might still get the occasional freeze, since I don't know how memory behaves for sure, and it seems like swapping might still happen with a new card. But with the CPU having lighter load, I suspect that the freezes will be much shorter.. or perhaps not noticeable at all.
And what I meant by $20 more, was in comparison to the previous video card that was in the $40 range. Since the new one is $10 less, it could go into the "RAM fund".. which would make the RAM a total of $20 extra. xP I was just trying to give you a point you could use for convincing your dad, although I dunno your situation so I guess maybe I shouldn't. D: Oh and don't worry about not posting in the right thread, it really doesn't matter in this case. :D
Oh yeah, also.. did you ever update the graphics driver on that computer? A new driver might be available: http://www.intel.com/p/en_US/support/detect/graphics