NHL doesn't have the authority to force the a team to move to a different market with out the owner agreeing to it. They would have to take away the franchise from him and again they can't just do that as they seem fit.
They probably can take it away if they work hard enough, I'm sure there's many many many legal things that would get them out, especially with AM embarrassment on the arena rent payment AKA making the league look bad/degrading value.
The ASU facility will be beautiful/State of the art I'm 100% sure, but it's still "bush league".
I also still think this won't be just a 3-4 year thing, I bet you it goes 6-10 years. Imagine them playing in a 5K arena for like 8 years. Gary absolutely will not give in if he agrees to the small arena, he's doubling down on his commitment (to AZ) at any costs.
This also F's anyone else trying to get public funds for an arena like Calgary for example... "one of your teams in a large market play in a 5K arena", Which is great, I'm not overly for public funds, I don't mind tax breaks and things like that. But Gary's strong arm is essentially gone forever, but I'm sure he's closer to the end of his career then the start, so I'm betting once this AZ arena is done, he retires.