The AHF looks to be intended to being done in addition to an organization's "traditional" league. Honestly, looks like a way to ensure that the rinks sell every single ice slot. The closest thing I can think of is the EJEPL (https://www.ejepl.net), which operates up and down the coast and is a way for teams to play a "split season" schedule and not have to be scrambling to fill game slots. Ashburn, Montgomery, Tomorrow's Ice, and Team Philadelphia have all played in EJEPL in the past.
The AHF has over 250 teams in the league providing high quality competition at every age group and level. AHF’s initial goal is to act as a supplemental Tier II league to rink owners who operate clubs in the DVHL, NJYHL and CBHL. The AHF provides high-quality, non-league games and showcases in the Mid-Atlantic uniquely catering to its member owned clubs.
The key word there is "initial", if they buy enough rinks and attract enough teams/organizations I could see it replacing some of those leagues down the road, but not in the near future. It will be interesting to see how long it takes before Allegheny and South Pointe stop attending local tournaments and traveling to these other member rinks to complete in "showcases" as opposed to tournaments.