Hi there! Perhaps you could update the drivers for your GPU. As you said, if it can run TF2 it should be able to run Project Kat as well - so it's most likely just a case of outdated drivers.
It depends on your GPU. For nVidia and AMD cards, it's as simple as going to their websites and downloading the latest version of the drivers. For Intel integrated graphics, it can be a little more complicated. I suggest you google instructions for your specific make ^^
