Atari 1975 1-6 player one-button horse racing arcade game. The first multiplayer one-button arcade videogame. Possibly the first commercial videogame with music.
1972 SEGA Grand National Race
SEGA's 1972 electromechanical horse racing game shares the same one-button control and Call to Post music as Steeplechase.
Toy electric horse racing games predate both Atari and SEGA's games and are often possible to play with a single ON/OFF switch. A forfeit for the loser made these games even more fun.
Off on a tangent, the first videogame music can be found in Christopher Strachy's Draughts from 1951.