While type I fibers (slow twitch) are recruited with all exercises, the question is which is used beyond that, IIa or IIb.
If the athlete has a high strength to bodyweight ratio, then the nervous system will only turn-on each successive muscle fiber type as needed. I would think a huge amount of IIb's would have to be used to hold the positions on the rings or horse. But all types are recruited when in working with high loads/accelerative movements.
I would think the parallel/uneven bars would use a mix of fibers, but mostly type IIa.
I would say most gymnastic movements tap into the type IIb's frequently just from looking at the muscular development of the athletes, let alone the explosive movements and static positions.