Many threads about cheeseformice have already been closed and I can't find much information about it anywhere so I figured Ill give this a try.
As many of you know cheeseformice has been closed for quite a while now, and api.micetigri.fr seems like the only thing that comes close at the moment.

Both of these services didn't seem to have anything to do with Atelier801 or transformice, but seemed to be completely built and moderated by players.

Now my question is if this API from which cheeseformice and micetigri retrieve their data is public? Are there any prerequisites one needs before being allowed to use the API or is this not possible at all? If so, then how did Cheeseformice do it?

Personally I think micetigri is a pretty incomplete website and I think if the API would be public many more implementations of a cheeseformice alternative would be made, just as I would like to do so myself.

Any information regarding this topic is welcome!

Users who can be trusted enough can be given the API if they ask permission through the proper channels and you will probably have to provide information on what you will be planning to do with the API once you receive it.

There was an announcement that is still relevant - you can follow the instructions in that thread to gain access to the "Stats API". If approved, this will give you read access to a MySQL database full of player's stats to use. I've extracted the first few thousand rows of each table to a Gist so you can see what the structure is like.

However, Atelier is planning on releasing a more appropriate public API at some point - although details haven't been confirmed on when this will be or where it is on their priority list.