This mode is strictly for local play (2 players) and does not natively support online or LAN play.
If you are using a version of the game that includes this expansion, here are some key technical points from the PCGamingWiki : Super.Meat.Boy.Race.Mode.Edition.rar
Periodic rotations of hand-picked chapters created by the community, often featuring extreme difficulty. Technical Details and Requirements This mode is strictly for local play (2
Players can manually choose the chapters they want to race in, including the more difficult "Dark World" variants. Super.Meat.Boy.Race.Mode.Edition.rar