Is my friend behaving badly by letting me know my ex-wife remarried when I've clearly told him I don't want to know anything about her?

Your friend is trying to subtly push your buttons and deriving pleasure by causing you pain.

Some people just like to gossip man, don't think too much of it. 

yeah get some dirt on his wife and it's payback time baby.

He just couldn't help himself . I dont think it is malicious.

Since you told him you had no interest, you should ask what purpose he had informing you. With that information, you can assess whether your friend's behavior was innocent or malicious.

Is he behaving badly? No. He's either not a very good listener, or he's just stupid. But there's no evil intent there.