I expected some turbulent meta-goofing to happen but he’s just emceeing the show.
He seems to be genuinely star struck. maybe he is, maybe he’s a big fan.
I couldn’t swear that this was the “gag” that Kaufman was going for, but back in the 70’s, Slim Whitman was kind of a joke. He was one of the first to sell records on TV in the middle of the night, along with Boxcar Willie. To the hip, just mentioning Slim Whitman was like mentioning Lawrence Welk or Montovani or something.
It would be like someone hosting a show on TV today and presenting Billy Mays as for a dramatic soliloquy.
I don’t think there IS any explanation that would make this hilarious- it’s just sort of oddly interesting in the same way that famous Bing Crosby-David Bowie duet of “The Little Drummer Boy” was.
I don’t remember that episode, but I remember the show itself. That was NBC’s old “Midnight Special,” and presumably Andy Kaufman was hired just as a standard comedian-host. And in THIS case, he seems to have been playing things straight, and behaving just like an ordinary comedian-host.
Knowing how bizarre Andy Kaufman often was, a viewer of that clip might keep watching, expecting something crazy to happen, or expecting Andy to do something zany from the wings. In this case, Andy doesn’t do anything at all.
PERHAPS (and this is a really big if) Andy Kaufman was the one who invited Slim WHitman on the show in the first place. IF so, that may have been the joke in itself. As Jack Batty says, back in the Seventies when this was taped, most Americans had NEVER heard Slim Whitman perform. I certainly hadn’t. I knew him only as a goofy looking guy who sold a “Greatest Hits” album on late-night TV commercials. He was regarded as a joke, the musical equivalent of Ron Popeil.
MAYBE Andy Kaufman thought it would be funny to have a cheesy, yodeling, aging country singer on a show aimed at young, hip rock fans.
And MAYBE, upon meeting Slim, Andy actually LIKED him. Sure, Andy could be a sneering, sarcastic jerk, but he could also be surprisingly sweet and sentimental, and he sometimes genuinely LOVED show biz kitsch. MAYBE he didn’t find Slim as ridiculous as fans assume he would.
This other clip seems to support the theory that Kaufman both genuinely liked Slim Whitman, while recognizing that he was worthy of ridicule.
And thinking of Andy as a comic would be a mistake. He was a performance artist whose performances sometimes were funny. He was perfectly capable of doing a performance that he found interesting–and keeping it up for an unlimited amount of time if he thought it was interesting–even if no one else thought so.
Nothing to add but that I kinda liked that performance by Whitman. Never heard of the guy before.
Looks to me like he’s just watching Slim play.
Nothing to add to the OP here either, except that the song was a favorite in my early teens. But 20 years later a Slim Whitman album was what we used to play a Christmas present trick on my daughter. We gave her the album she wanted, but she got Slim first. She had peeked at the gift and told her brother she’d have no problem acting surprised when she opened it. She didn’t have to act. 
In Bob Zmuda’s biography on Kaufman, Zmuda mentioned that at times, if you were telling an interesting story to Andy, he would go into a sort of wide-eyed, trance like state where he wouldn’t just be listening to your story but sort of mentally reliving it and recording it in his mind. I say that’s what’s going on here and you can see that Andy hand internalized Whitman’s nuances and pulls off a very good impersonation in the Letterman clip -albeit while wearing what looks like a man-diaper.