Some horses will "belch." Others with gastrointestinal problems preventing fluid from getting out of the stomach through the small intestine will spontaneously reflux. That being said cribbers will crib on anything. Here is a quote from The Horse publication:
Rhythmic actions (such as weaving, stall walking, and cribbing) performed by a confined animal develop in response to stress and are a type of obsessive-compulsive behavior that is difficult to halt. When a horse develops a compulsion, it's a clue that his needs for social interaction, security, mobility, natural feeding behavior, etc., are not being met. Once established, however, the behavior becomes a need in itself, and the horse insists on continuing it.
Twenty years ago, scientists at Tufts University led by Nicholas Dodman, BVMA, MRCVS, DVA, MAPBC, Dipl. ACVA ACVB, discovered why horses crib and why the habit is so persistent. Whenever an animal or human is stressed and engages in some type of repetitive activity as an outlet for pent-up energy, morphine-like proteins called endorphins are released in the brain. The constant activity triggers the endorphin release. The animal will keep up the habit even when no longer confined or stressed because he finds that repeating the pattern produces these calming "opiods" that suppress pain and create a pleasurable sensation.
Horses seem relaxed after a cribbing session. As the act of cribbing causes a temporary sedating effect, the horse becomes addicted to his internal chemicals. He craves the endorphins and gets his "fix" by performing the repetitive behavior. Some horses will actually stop eating and crib during the middle of a meal. This behavior is truly an addiction rather than just a "bad habit."
Since the horse in question is a cribber it may be trying to crib on the cross-ties. I have a mare that will "chew" on rope but I think its more of a curiousity thing as in "gee, I wonder what that tastes like" since she isn't a cribber. She seems to like cotton robe more than nylon so it may be it does taste good.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France