


So this is an issue with this game and Steam in general, and will do the same thing on any PC under Windows or Linux. The game does not like Steam Input for multiplayer, and the first controller will control all players. Turn off Steam Input for this game (in the properties for the game, in the desktop version of the Steam client). Don't worry, you can still reconfigure the controls if you want. This issue only affects local multiplayer.
There is no online multiplayer really, but there are online leader boards and they work fine.
Once Steam Input is turned off, works fine.
Note that the old arcade version of the game is also provided, but that pegs the game speed to the refresh rate (the main game does not do this). This is true on Windows too, and on any PC. Switch it to 60Hz for the old game version.