Am I the only one who has written a game - actually two games - *around* animal riding?
Gurps Horseclans?
I wouldn't say so. I have GURPS Horseclans, though it's in storage, since I don't find it useful for much other than playing in that campaign setting. Now, you could certainly play a GURPS Horseclans game and have it centered around horse riding, but I don't remember GURPS Horseclans really adding a whole lot in the way of rules around riding, though I might be forgetting a little bit. It was one of the first GURPS worldbooks and so is for 1st edition, and I doubt it adds anything in the way of horse rules that isn't done as well or better in 3rd and 4th edition Basic, let alone the Roleplayer article with the super-detailed horse rules.
A GURPS Wild West, or even many fantasy/medieval or Renaissance GURPS campaigns could be fairly horse-oriented if most of the characters and many of the plots were so oriented.
But none of that makes it, I'd say, a "game *around* animal riding" *per se* (at least, not the way it sounded to me when you wrote that), unless the GM chooses to emphasize that.
Add me to the list of people quite curious about what your animal-riding-centric games are like.
Oh, and I just went and grabbed the James Bond basic book and the Q manual. Interesting chase rules, though I'm pretty disappointed in the low grain of the vehicle stats, where Performance Modifier only ranges from -1 to +2, with most cars being 0 or +1, and even then some values seem questionable to me. I'd have to tweak the stats to give more difference between car types, and would probably want to add more types of stats. I get though that that might undermine the James Bond feel, where it's more important to describe how stylishly or amusingly you do stuff, and to have Bond be able to use any vehicle to embarrass people due to his raw uberskills.
(Games that allow and focus on dragon-riding (...) could also qualify, sort of. ;-) )