I have very few of these.
Survive: Escape From Atlantis has been mentioned, but I don’t consider that to be a racing game at all.
Camel Up is certainly about racing, thematically; but the point is that players have very little control over the order in which the camels finish, so… not a racing game?
Rallyman GT is as much a puzzle game as a racing game, but I think it qualifies.
K2 has your pair of mountaineers racing to climb higher than anyone else without perishing. It’s a little bit like Flamme Rouge, but with slightly higher thematic stakes.
Curiously enough, my pick is: Judge Dredd: The Cursed Earth – the 2000AD-themed adaptation of The Lost Expedition. TLE itself wouldn’t qualify because it lacks the chase element, but JDTCE has you racing to hunt down a target before an opponent who begins the game with a head start. So you have to firstly catch your opponent and then manage to stay ahead of them until you reach the target. If you reach the target. That’s a big “if”.