There's one line I never understand, and that's when (according to what he tells the vet) Columbo was told that the first time Tomlin disappeared, it turned out that he just went bowling. I don't mean it as a cultural thing, but I don't understand a Russian chess master using BOWLING as an excuse for where he was. Of course, as a kind of "irony," it ties in with Columbo himself wanting to go bowling just before he was called in on the case, but I still don't get it. Is that actually what Tomlin told them when he got back to the hotel?

It is a demonstration of his down- to - earth personality. He enjoys the activities of common folks, not the elite.
Yes, He was telling the truth.