Your PC being 32-bit means that your operating system is 32-bit. Some games like Dragon Age Inquisition require a 64 bit OS to run. Your card will not work with games that have this limitation, but that's due to your OS, not your graphics card.
The 64-bit of your card is the memory interface. Without getting too technical, this can rage all the way up to 512-bit in current graphics cards, and is only an indirect measurement of how much memory bandwidth the graphics card has. This has nothing to do with running on a 32-bit or 64-bit OS.
The only limitation for your card not working that I can think of, is if you have an extremely old or non-windows operating system, that your card doesn't have drivers for.