As for the connection to Fallout 3, really it's just because Fallout 3 transported a lot of content from the first two games regardless of how tenuous the connection was.
In New Vegas, the Rangers obviously are a more natural fit to the game and as a continuation from the reference in the original. In FNV the Rangers were an independent group which has been absorbed by the NCR, though they still have a lot of autonomy. That's what that big statue at Interstate 15 is about.
I'm actually a little shocked there aren't (to my knowledge) any Roger's Rangers references in Fallout 4, given that the are Minutemen LARPing around.