There are a lot of games that sold incredibly well and have millions of people playing it everyday, but a lot of them doesn't last long.
Angry Bird is a good example, Destiny is also a good example, those game made tons of money, but in the end of the day people don't really remember or even like them.
What I am saying is, Battleground is a extremely fun game but it isn't the end all be all that's gonna sell any console like crazy. Millions of people bought a NS for BOTW, but only a small portion of people will actually buy a [insert console name] for Battleground. Especially consider that most computer can run the game already.
What people...where... Angry Birds has had numerous sequels, licensed franchise spin-offs (like that Star Wars and Transformers stuff "nobody remembers or likes"), a tv series, a movie and a toy line. Destiny's active userbase across all platforms is probably far greater than niche Japanese games combined played on ps4s.
I wonder how MS markets this and the length for the timed exclusivity.