Plus no it is not black humour or irony, both of which I “get” and enjoy.
It was a misogynist joke in extremely bad taste, that revealed him as a complete arse, and is quite informative about his character. Since he obviously expected that his audience/followers consisted of similar arses who would find the joke funny, it is also revealing about them.
It is also not about intelligence, but about attitudes to women, and a general sense of decency that should tell you whether a joke is on or not.
I’m sorry but you clearly do not get it! Also you do not know the context with which it was written by him so how you can judge him on it is beyond me.
There are loads of scenarios where he might have written that as a private joke, for example, say he’d been having a chat in the changing room and said something which someone else misheard as “just battered the wife”. They all had a laugh about how it was misheard and how random a thin g it would have been to say. Later he then writes on twitterbook “Just battered the wife”, knowing his mates would get the joke.
The above scenario is one of hundreds of possibilities, it does not tell you anything about his attitude to women.
If you don’t get that then as I say, you don’t get it.