Yes, Blacknut supports local multiplayer for certain games. An entire section of the library is dedicated to multiplayer games that you can play together on the same screen, in co-op mode or head-to-head.
The icons next to each game let you easily see which games you can play in local multiplayer:
Online multiplayer gaming (playing against users in other locations via the Blacknut app) is currently in development and will be available to play soon.