I couldn't find any evidence of anyone else coming up with something quite like this, but this idea was pretty organic, so it wouldn't surprise me if someone had beaten me to it. If so, I apologize, but as far as I'm aware, this is a fairly original idea (beyond, you know, being a merger of two existing sports).
As for how this came to be, I was around while a relative of mine was switching back and forth between watching baseball and golf. This was the resulting thought process:
Etc, so on and so forth, up until I thought "it would amuse me if Noah came up with this".
I also like the idea that the opposing team wouldn't have a person for each ring, and some freedom to move around so long as they're not within the rings or on the lines indicating the rings (the lines being painted a bit thick). As such, it would take some foresight to ideally position themselves, and the pitcher and batter would need to decide where to try and go for in part based on what the other team was doing, too.