them starts with a woman taking a bath. She's having a conversation with
her cat, who jumps up on a vanity table next to the tub, and then knocks
something electrical into the tub, electrocuting her. (They never show
the gory details - in this one, you just see her feet shaking.) Anyway,
I braced myself for a sad moment where the cat starts crying for his
dead human, but instead, when the camera cuts back to the cat, he's
sitting there washing himself.

Yes, I remember that episode. I thought it was funny, too. I love the
subtle, but oh so black, humour in that show.

Why is it funny that the cat was licking itself?
Really, I'm not being difficult. Thanks

The humor, at least for me, comes from the cat being totally unaffected
by the momentous event that he has just caused.