In eg: https://itch.io/games 
The row of tags (about 3 or 4th row), it would be very useful to also be able to exclude tags.

So you can make a search like:
"Atmospheric, -Horror"
Meaning it shows all "Atmospheric" games, but excludes all games that contains "Horror".
(Even if the game contains both "Atmospheric" & "Horror" it will still be excluded. Possibly with an option to change that behavior for that result to be included anyway)

Currently, it seams to only be possible to include tags, but not exclude tags.

Yes, that's how itch.io is designed to work. See this recent topic, and the long discussions about this over the years.