Nintendo has added minor cooperative modes to a number of its single player games in the past, perhaps most notably with the Mario Galaxy games, which lets a secondary player collect ammunition and stars for the main player. Things are a little more interactive and hands-on in Super Mario Odyssey though, as the recent Nintendo minute video shows.
In Odyssey, one player takes on the role of Mario, while the other controls Cappy. That second player can fly around at will and provide additional functions, like picking up coins, cleaning up dangerous areas, knocking around rocks and other terrain features and more.
As a cooperative game mode though, you do need to act as a team. Although there are ways that Cappy can mess with Mario, the secondary player can help Mario along the way too. What he can't do though, is independently take over an enemy, as Cappy does in exclusively single player runs of the game. When Mario needs to control an enemy with Cappy, he does so as usual, and Cappy can then fly around by itself afterwards.
It doesn't make a whole lot of sense, but then the idea of Cappy possessing various characters is a little suspect anyway. Does that mean that Mario has been controlled by his hat the entire time?