Seems like competitive clubs would be those where there is some sort of capacity limit relative to the number of students who want to join.
Perhaps some cases involve skill based clubs like sports teams or performing arts groups. Perhaps others involve situations where exclusivity is desired for resume-building toward competitive post-graduation goals, like the pre-IB/MC and pre-med clubs.
Regarding LACs, it may be that their smaller size means that any given capacity-limited club is less likely to overflow and need to be selective.