Athleticism has always played a big part in Barney's work, all the way back to the beginning, when he did installation pieces which involved him climbing across the ceiling. I can't remember what exactly this is supposed to symbolize (a little help here, Jonno?), but it's documented in last year's Cremaster book published for the Guggenheim Cremaster exhibit.

In the Drawing Restraint series, Barney used physical limitations to alter the marks he was making while drawing. Climbing was a part of this series, as well as weight-lifting, etc.... several themes that crop up throughout the Cremaster Cycle. The scene in the Order with the Sphinx looks a lot like photos of the Drawing Restraint series.
His work in the Venice Biennale (i think?) in 1993 involved installing surveillance cameras in the building that housed the exhibit and positioning them in backrooms, the basement and an elevator shaft. the cameras were attached to a series of monitors that museum patrons could watch. Barney's performance consisted of making his way to the elevator shaft and climbing it. the art was a rebroadcast of an act that took place in the museum, but seen only by proxy. the work talked about effort and restraint, society and the spectacle, and the gulf between life and art. but sometimes i think he just wanted to climb the elevator shaft and figured out a way for "them" to let him do it as "art". which is a good enough reason for me...