This sub-game is stated to be a sort of "what if" scenario or alternate universe/timeline; the same is likely true for the other Meta Knightmare sub-games.
Meta Knight retains many abilities and attacks from Meta Knightmare Ultra. He is able to use Galaxia (which applies fiery effects) and the Knight Spin (which applies icy effects). Special Moves from Meta Knightmare Ultra also return. Meta Knight has new attacks as well as slightly more power and speed in this sub-game.
Meta Knight can accumulate Meta Points (by defeating enemies), and can store a total of 50 points. He can spend these points to use these moves:
Meta Knight's movement speed is increased for a short period.
Completely replenishes Meta Knight's health.
Meta Knight unleashes a powerful attack with Galaxia.
Meta Knight summons members of the Meta-Knights for a powerful attack.
Stages are compiled in one level and at the end of each, a time will be shown.
At the end of each level, there are save points that also refill all of Meta Knight's lost health. These are scattered at around the halfway point in each level. In the case of Level 6, there's another save point just before the boss.
End of spoilers
Kirby takes a nap during the events of this mode, explaining his absence from the sub-game's story.