Hi,
I don't know what to do and I didn't find any help with google.

I wanted to play Laputa - Castle in the Sky track. So I downloaded it and put it in Trackmania/Maps/Downloaded. However the game claims that this map is not suitable. Tried it with a lot of other random maps and it still didn't work.

I have Standard access and reinstalled game once.

Can anyone help me out?

The map you're referring to is for TrackMania 2 Stadium.

All the maps on this site (tm.mania-exchange.com) are for TrackMania 2.

If you want to play the map, you'll need to buy TrackMania 2 Stadium.

You mention that you have Standard access. That would be for Trackmania (2020).
For tracks made in Trackmania (2020), visit Trackmania Exchange.