The key thing is that no legislature ever voted to permit the "state" to seize these properties. The law that permitted what is being called eminent domain granted seizure powers only in the case that the land was condemned. So the "state" (actually Jerry Jones, of course) is taking property by condemning the land. In other words, by ruling that the land is unfit to be dwelled in.
Once authority is given to a state to seize a land based on conditions set by that state, the state will inevitably be corrupted by that authority. THAT is why the founding explicitly denied the state that authority. It was NOT because it was concerned about people being asked to sacrifice for the good of the state. If it truly were for the greater good, then the state seizure of personal property could be justified. The issue is that the founding fathers recognized that states were not God; they were inherently corruptible. Thus freedoms and protections are granted to individuals, not because they believed that it was good that individuals did bad. That belief would be simply illogical. Rather, they believed that the state possessing such authority to determine for others what was good or bad would be corrupted by such authority, and thus the good of the many would be destroyed as well. And so the founding fathers created a system which sought the common good by ensuring that the manifold pursuit of individual interests led to the common good.
I don't know that voting in legislature is necessary, although I am probably wrong. I think in this case, the plans just needed to be approved by a voting quorum of the city government.
Takings can actually occur in three ways: actual condemnation for safety or health reasons, developments to land or buildings which restrict access to property and cause hardship upon the owner, or takings of property for public use with just compensation. All levels of government -- local, state, and federal -- must adhere to the principles of the due process clause of the 14th Amendment. In the past, SCOTUS usually ruled that certain strictly authored zoning restrictions or building permits were violations of the takings clause, mainly because the government must prove a tight fit between the taking and its purpose.
I just don't see this ending as quickly as Jones might wish, although in the end he'll probably prevail.