You usually need a graphics card to be able to use a computer normally, playing tremulous with no video can be tricky if you don't have good headphones/speakers and something like ventrillo, gamecomm, or teamspeak.
However, most video cards can handle tremulous, it uses the Quake 3 engine which is from late 1999. What is your computer's onboard video card? (the one built in)
Most likely you'll be able to run it, if not then you can purchase a cheap NVIDIA RIVA TNT 2 for PCI or VGA (whichever you have free to use) for around $10-25 and play decently on that.