This seems like an odd thing to exist, period, let alone to run against the Olympics. Then again, coverage was different then; NBC had just one hour of highlights in prime time. After 8:00, that's it, and it's time for a repeat screening of 1965's A Rage to Live.
Back to Budapest, though. Bill Bixby and Brandon Cruz actually went to Hungary and shot some footage of them touring the city. The special commemorates "the opening gala of the new completely automated Grand Palace of Circus," according to the listings at Ultimate 70s.com. The Fest was a regular event featuring various circus acts, and it apparently continues to this day. This special was shot at the 1971 version.
I had a hard time finding information about this special, which isn't in one of my go-to reference books, but I did see an enthusiastic review in the "TV Scout" column in the Suffolk-News Herald. The note mentions the performing hippo, a trapeze artist who stands on his head, and highlights, "Bixby participating with Miss Alda, the world's finest lady barber. Wait till you see her and Bill's expression as he watches her prepare to work on him." It seems less enthusiastic about the travelogue component: "Also a few shots of Bixby and Cruz wandering around Budapest, where this was filmed."
The column also notes that producer Greg Garrison was working up till air on the Feldman show, so no one was really sure what would be in the 30-minute distillation of what was originally going to be the first of a series of 90-minute episodes. Art Carney and others "have a chance of making it on"!
(Note: This post should have run February 7 but is premiering February 8 because of technical difficulties, as in I somehow had difficulty and botched the posting)