Yes, thats GTA3 being described there... Why do I feel that you are trying to be sarcastic?
The Turismo Race(s) that Hippo speaks of, are on the very first Island of GTA3. You take part in them by doing missions for the Diablo's... Answer the phone....
Thinking about it, the closest you can get to Dirt Track Racing in GTA3 are the special Hummer missions that are scattered on each island... and in those missions, the only racing you do is against the clock.
Suprised you havent heard of GTA: Vice City...