I have found with Disney they are very good with dealing with problems without people seeing. I love people watching and have seen, on a few occasions, a rambunctious person guided away to a quieter corner where they were dealt with.
I remember one in particular. We were on the great movie ride and a group of young adults were on. One had a shirt that had mickey gloves on it with the middle fingers showing. I'm guessing he wore a coat through security and took it off in the park. Anyway, after the ride, and in the gist shop various 'guests' inconspicuously blocked paths and he was slowly moved to a corner near an exit (I don't think he realized it was happening). A CM approached him and I overheard him, very politely, request the male had two options. He would buy him a shirt he could wear and take off the one he had on or he could leave. The person accepted the shirt and went to change. The great part is that when I looked around I could see about 4 or 5 suits hanging in the weeds watching. If things got out of control they would have swept him away out the back very quickly.
While what OP saw is truly obnoxious, frustrating, and doesn't belong in Disney, what would the cast member do? Let's say he gave him warnings and the guy doesn't stop. Should they call in security there? Do they drag him off the vehicle? What if he doesn't want to go? Do you want your kids watching a fight between security and a drunk patron? The best course on their part is to let it play out and the can deal with him off the ride where it is away from the 'magic'.
Having said that, I do believe if it is bad enough they will do with it appropriately right then and there. Security is very much about risk management. What do we gain an what do we lose by dealing with things in a certain manner at a certain time.
I know it would never happen but I think a Disney security TV show would be amazing. All the stuff that goes on that we never see.
ETA sorry I realized after the drunk person was not from the OP post