as a puzzle game, I feel this would be better without the full text explaining every mechanic in the game, although I do like the way you did so unconventionally. I think you could probably keep that in if you have all of it be closer to the vibe of "Also, try to avoid from gray spot with a black center. Once you lose, you can restart level with "R" letter."
In terms of being an ice puzzle variant, I would like you to know that ice puzzles are one of the hardest types of puzzles to make interesting and not trivial. I think your mechanics definitely helped alleviate some of what makes ice puzzles so trivial, that being the lack of movement options that aren't just going back where you came from. And an interesting take to, adding a lock and key system to encourage backtracking. I would suggest adding some keys that are impossible to come back from though, requiring players to read the level and interpret its logic more. The needing to manage multiple players also has the potential to be interesting, it wouldn't be too difficult to attempt making a multiplayer synchronization maze, where there are many holes and only a few paths without holes, but I feel like that's not what you were going for here. nonetheless, I feel some people would appreciate the difficulty, as long as it doesn't gatekeep later levels of the game.
If you ever decide to add a new mechanic, I would suggest a reusable toggle button. Even if for a different game, I find that they can lead to a massive amount of deductive logic for a comparatively small level of effort.