You can play normal game modes against AI opponents, but none of them seem terribly bright, and they're laughably bad at the mini-games that give boosts. (shacknews.com)
The 4v4 multiplayer will have your normal game modes you would expect from a FPS game nowadays, your Team Deathmatch, Free - For - All, and more. (thatvideogameblog.com)
Besides the normal game mode, Super Mario Run also comes with a couple of other game modes, one of which is called Toad's Rally where you'll be trying to impress a bunch of Toads by collecting coins and performing tricks, competing with other players for the most impressed Toads. (droidgamers.com)