There's a difference between being a marriage minded man and being a sadly desperate man.
In my mind, a truly marriage minded man (one who's a great catch, anyway) isn't discussing marriage on the first date nor displaying desperate behavior by giving ultimatums.
A good marriage minded man is selective. He's looking for a life partner and wants to get to know you first before letting his intentions be known.
When I was single, any guy talking about marriage and babies (or asking too many questions on the subject) on the first date (or too early in dating), earned a shiny new "RED FLAG!" from me. Smiley doesn't do desperate. I'm not trying to be someone's "anybody". No ma'am.
IMO, a good marriage minded man is one who makes it clear that he's not playing games right before he commits to you. He's complete without you, but has decided that he wants to spend his life with YOU... the woman he has grown to LOVE.
A desperate man is trying to find somebody, anybody, to marry and start a family with ASAP! Every other first date is "the one". These men are trying to fill a void. That can be dangerous.