I think of it as basically a garden-path joke.

Incidentally I've noticed that jokes structured like this have become so common in UK comedy shows that the punchline is often unnecessary or even omitted.

I don't know if the type of humor itself has a name, but the technique it employs is misdirection, of which there are many variations such as posing a question to 1 of 2 very different people, when the more suitable target (to audience) starts to answer, asker then says "I wasn't talking to you"