A description of what the schema.org project is for can be found here - https://schema.org . On Habré, this is a rare guest, there was not even a special hub for him.
I know that Yandex tried to use schema.org ... They apparently do not use this part.
Relations
https://schema.org/Library , https://schema.org/ExerciseGym - both refer themselves to https://schema.org/LocalBusiness .
LocalBusiness refers itself to two objects at once (this is where the schema.org feature is): https://schema.org/Organization and https://schema.org/Place
Dictionaries
https://www.oxfordlearnersdictionaries.com/definition/english/gym?q=Gym (one meaning is place, the other is organization)
https://dictionary.cambridge.org/us/dictionary/english/gym (one meaning uses ambiguous word "club", another about the place)
Checking with dictionaries can be overwhelmed, but I see no reason for this ...