Here's the clip
I know it's probably a pretty trivial question for this sub but I don't know where else to post. Given the reputation this routine has I assumed it would have the audience in stitches
Who's On First was (is!) uproariously funny! Here is a clip with the audience laughing as you would expect. The issue is that the video you specifically are highlighting here isn't a performance at a comedy club, it is a scene from a film, their 1945 flick The Naughty Nineties. The reason the audience isn't laughing is a very simple one. They were told not to.
The skit is one of the greatest pieces of comedy in the American tradition, and depends on excellent timing and "rapid-fire speed" by both Lou and Bud, so for these scene where they shoehorned in their most famous routine for the film, it was done in real time, with two cameras. You actually can hear slight bits of laughter at points because the camera crew themselves are having a tough time not cracking up, which Jean Yarbrough left in as a little Easter egg tribute. There were forty extras on set though for the audience, and they were told not to laugh because it would ruin the dialogue. It was originally planned that there would be "strategically placed giggles" added in after the fact, we can presume at places where it wouldn't interrupt the flow of the routine, but Yarbrough decided against it in the end.
Nollen doesn't say why, unfortunately, but we can speculate at least that given the rapid fire of the routine, it was hard to find clear spots to fit it in, and leaving in the crew sounds was a subtle nod in any case to the fact the whole thing was hilarious. Certainly film audiences agreed, such as exemplified in the Herald Tribune's review that called the segment - their first performance of the famed skit on film "the brighest spot in the film".
Sources
Cox, Stephen & John Lofflin. The Abbott & Costello Story. Cumberland House, 1997.
Nollen, Scott Allen. Abbott and Costello on the Home Front: A Critical Study of the Wartime Films. McFarland, 2009.
Guernsey, Otis L. ,Jr. "On the Screen: 'The Naughty Nineties'' Criterion." New York Herald Tribune, Jun 21, 1945,
As detailed in Abbot and Costello on the Home Front, this was a filmed version of their famous burlesque routine for the movie, Naughty Nineties. It is not a real live audience. The people in the audience were extras that were instructed NOT to laugh. And you can still hear little giggles in the audio that made it into the final cut.
To hear a proper live audience reaction to this particular bit, I would check out this performance in 1953 from their TV show.