"Sport is the old word for "fun," which included "sex," which includes prostitiution.

In the U.S. especially, the meaning was broadened in the nineteenth century to include gambling.

The verb "to sport" related to all these things.

So a "sporting man" could be a man who devotes himself to fun (including actual sports), gambling, and/or commercial sex.

It depends on the context.

The Boston burglar was presumably a "wild and wicked youth."

In the U.S., however, a "sportsman" (when not a hunter or athlete) was specifically a pimp. A "sporting girl" or "sporting woman" was always a prostitute.

The closest current synonym for "sporting man" may be "player," which covers most of the same activities in a comparably nonspecific way.