#1. To make a statement to WWE

If you saw Jon Moxley's post-Double or Nothing promo, it's clear as to how fired up he is and just how motivated he is. You can watch it for yourself below.
Did you know a top WWE Superstar just wrestled outside the company? More details HERE
He claims he's there for a paradigm shift and to give the industry a much-needed "facelift". It was clear that his "flipping off" after the show was also a message to WWE. He truly viewed it as a prison to him and only now are people truly realizing why he left and why staying was simply not an option for him.
Moxley is there to make a statement and AEW is just one part of it. By signing with NJPW as well, Jon Moxley is putting out a clear statement to WWE that not only does he not need them but there are plenty of others who are willing to give him the opportunities that he deserves.