Regarding the relationship between AEW and New Japan Pro Wrestling, according to several sources at this point it is limited to a storyline involving a shot at the AEW World title in tonight's Tokyo Dome match with champion Chris Jericho and Hiroshi Tanahashi.
Jericho, Tanahashi, and Gedo had the idea to use the possible shot at the AEW title to add intrigue to the Wrestle Kingdom 14. The storyline is that if Tanahashi wins, he gets a title shot at a later date.
If Tanahashi wins, it would obviously mean a second step has been approved in this angle because Jericho has not lost a singles match anywhere in the world since Dominion to Kazuchika Okada. AEW has the idea of protecting its World title, like New Japan does with the IWGP Heavyweight title, in the sense the champion would not be allowed to lose working for another promotion unless it is an approved key storyline idea.
Tony Khan and Rocky Romero were also involved in this deal as far as Khan approving and working with Romero on the usage of the belt in the storyline. Khan made the decision to allow it for the New Japan show but that it won't be used as part of AEW storyline, mentioned within AEW on television, or on social media by the company.
It is not clear if Jon Moxley's IWGP United States Heavyweight title win earlier today over Lance Archer will be brought up on AEW television. Because of a lack of relationship between the sides, his previous US title reign was not acknowledged in AEW. The only outside titles AEW mentions are those of AAA, as those companies have a formal working deal in place.
Jericho and Moxley have it in their AEW contracts that they can work with New Japan as long as it doesn't conflict with an AEW date.