Minecraft is available to play both offline without an Internet connection and online in multiplayer, Internet-based versions. Circle manages Minecraft differently depending on how a person is playing or connected to others, so here are some specifics.
Playing multiplayer mode on a local network can be managed by your Circle device. While the game play does not require actually going all the way online, the connection between devices on that local network is seen by your Circle device, and Circle settings will be applied.
Online multiplayer (includes solo player online playing with others)
The Circle device is able to know when a device is going online. When someone goes online to play Minecraft and joins a known Minecraft server, the Circle device tracks that game play and applies normal filtering and time limit parameters. Note that your Circle device does not know many Minecraft servers because they are set up by individual players.
Pausing and BedTime mode will always manage this kind of Minecraft game play.
Solo offline play
Playing Minecraft in solo mode does not require an Internet connection. As such, the Circle device does not see any of that Minecraft play and your Circle settings will not be applied.