Uck. There is a similar man at my gym. There is never any suggestion that he is trying things on in a 'chat up' kind of a way, it really is all about using people for conversation/interaction. But it is so extremely insensitively done, with such extreme entitlement. Question after very direct question, and zero self-correction when I try to give all the usual hints of just wanting to be in my own headspace.
The first time he did it to me, I eventually felt the need to give him a very polite but explicit statement that I didn't want to talk. I said something like "Sorry, but the sauna is a quiet time for me and I don't really want to chat."
He did stop, but a few minutes later, as he left the sauna, he burst out with a criticism of me, saying that I was rude and cold.
I think that low lighting, no glasses, and poor facial memory means that he doesn't remember who I am, and the other day I got the same overly-direct and insistent questioning. I just stonewalled as much as my conditioning allows me too - the very briefest nod, a single word, and pointedly looking away. He looked very disorientated but then lasered in on other poor souls.
TBH, from several chances to observe him, I think he does it to men and women equally. However, his female victims are much more likely to feel trapped in a conversation that is entirely dominated by him and continues regardless of their real interest.
He is in his seventies (I'm in my 60s, so he's not much older than me), generally seeming alert and intelligent, and has had a professional working life. Clearly insensitive to social cues, but, equally clearly, able to correct for that if he chose to. I mean, he evidently has the capacity to say to himself "Ok, l I don't get the cues, but I know there are rules that I should follow, so to avoid annoying people I should make sure they they are actively talking back to me, and that I don't talk for too long.'