I still don’t get the principle

Faire de -- this can be used with all sports and means that, generally, you're involved in this sport. Some sports can only be used with faire de, as, in French, you cannot "play" horseback riding or "play" skiing. Jouer à is mostly reserved for sports you are competing against an opponent.

Je fais de la danse. -- "I engage in dancing."
Je danse. -- I'm dancing (right now).

Je fais de la natation. -- "I participate in swimming activities."
Je nage. -- I'm swimming. (As in: I'm in the pool right now.)

Je fais du basket. -- "I am engaged in basketball." (As in: I'm in a team)
Je joue au basket. -- I'm playing basketball. (I'm on the court right now.)