If you can run TF2 I don't see why your PC couldn't support a basic graphics card like that, your one is just a bit outdated.
Calling a graphic card that is about 10 years old "a bit outdated" is pretty generous.
The main reason why your computer can run TF2 and not Super Meat Boy is because the former still has DirectX 8 support in order to make it accessible to older hardware. Super Meat Boy requires at least a DirectX 9 compatible graphic card.
So yeah, your graphic card is too old to run the game. You'll definitely need to upgrade it if you want to play. This chart should help you find such a card (at minimum you'll need a Radeon 9500, which probably could be bought for cheap on Ebay)http://en.wikipedia.org/wiki/Pixel_shader#Hardware