So, if I get Roon, would I be doing the same thing from the Roon app on my laptop or phone?
You would be controlling it from your laptop or phone but, as the previous poster says, the Roon Core is doing the work and it will reside on your laptop (or other computer).
Would I be completely bypassing "Manic Moose"? and doing everything on the Roon app, including such things as volume and song selection?
Yes. I will be using the BDP (if it is Roon Approved) as an endpoint/DAC.
I understand that Roon is an effective organizer of music from multiple sources; is it also a "media player??
?? What media do you have in mind? Roon is a music player, library manager and streamer application. It will not support video, TV, etc.