Any game that involves active interaction with the music is a Rhythm game. That includes games where the musical beat affects game play.
Beat Chaser 2 [10.000] Votes: 2.64
Beat Chaser 2 is a combination of bullet hell and rhythm games. The music will affect the motion of the bullets. You can choose your own mp3 file or use the prepared songs.
Super Crazy Guitar Maniac Deluxe 4 [10.000] Votes: 21.62
After a long wait, Super Crazy Guitar Maniac Deluxe is finally back! There are 55 achievements, 14 guitars, 15 songs, and some hidden challenges. Time to pick up that guitar again!
Vector Stunt [9.870] Votes: 69.07
Do jumps and stunts to your favorite music in this retro-styled 3D game. Vector Stunt lets you load your own mp3s and uses the music to influence gameplay.
Musaic Box [9.772] Votes: 39.55
Uncover all of your grandfather's sheet music hidden amongst a treasure trove of gorgeous antiques and musical relics. Piece these special compositions together and unleash their musical secrets.
Platcore [9.740] Votes: 19.45
Platcore is an avoider game where you play as a Platbot, which is a testing robot for Platcore. Platcore will be using you to test their newest products, which come in the form of things which aren't friendly (lasers, turrets, even bigger lasers... you get the idea). The game's soundtrack is synced to the Platcore AI, so when the soundtrack goes boom, something else is going boom, and it's likely to hit you in the face.
Music Catch 2 [9.731] Votes: 85.58
Catch all the new shapes, patterns, motions, and songs in the sequel to one of the most popular music games to date. Your task is simple. Collect more shapes to receive more points.
Music Catch [9.684] Votes: 79.04
Catch the colorful shapes that appear when the music plays! The more shapes you collect, the more points you get. Yellow shapes give you a bonus and multiply your points, but watch out for red shapes!
Pulsr [9.609] Votes: 23.04
Pulsr lets you create music loops and beats by chain reactions. With a simple interface and an innovative concept of musical creation, anybody can create music in no time.
Music Ping [9.605] Votes: 22.76
Fourth (and last that I could find) of Coolio-Niato's Music MiniGamez. Includes three levels, trophy cases and high score tables. Enjoy songs by cornandbeans and ParagonX9. See if you can get gold trophies on all 3 levels!
Dance Floor Destroyer [9.500] Votes: 6
Choose your DJ or import your own Meez avatar to do the spinning. You are a superstar DJ looking to keep the party rockin'. Your perfect beats will drive the vibe high and keep it there. Let the vibe go too low and you will feel it from the crowd.