Any secret to getting the game to recognize my controller as... a controller?

Assuming you plugged in the controller and gave Windows a chance to detect it before running the game, you'll also need to pop into the game's options and set the control method to "Joypad" or "Joystick", the latter allowing you analogue control of the bike's steering, though not the acceleration and brake, it seems.

Don't forget to remap the controls to a layout you're comfortable with, as well.

I know this thread is quite old, but I had this problem and, since no one posted the solution, I'll do it. It may help someone in the future.

The controller you want to use with the game (Xbox 360 or otherwise) needs to be set as the primary controller in Windows.

1.- Open the Start menu, type "joy.cpl", then press Enter.
2.- Push "Advanced".
3.- From the dropdown list, locate the controller and then push OK.

Note that the game only recognize 2 axis and 8 buttons, so you'll have to deal with that limitation.

EDIT: I wanted to post a link, but the forum really doesn't like the format:

[url=http://pcgamingwiki.com/wiki/Glossary:Controller]http://pcgamingwiki.com/wiki/Glossary:Controller[/url] <- Primary device