There is going to be significantly more grey area here then many you are implying. If it was as basic of a dispute as the Yotes truly owe $1.6MM the league would no way ever allow it to get to the point where the city was threatening to kick the team out.
I am 100% sure there is much more to the story than what is being tweeted out. I am also 100% sure the team will not be locked out of the arena.
The tweet, to me, comes across as nothing more than the city generating negative publicity for the team. I wont claim to be a lawyer but i would assume there would have to be some sort of legal filing for this to happen, as the debt is "tax" debt which means the city is taking action to enforce tax law. Any legal filing would be publicly available, since no one has posted anything I am going to assume it does not exist.
As far as this "killing" the Tempe deal, again there is obviously going to be more to this than the Yotes being far enough behind on tax payments for action to be taken, as once again the league would not allow it to get to the point where legal action could be taken.
Lets wait for more info to come out before jumping to conclusions.