A public venue is different - it indisputably falls under the eminent domain power. There are two categories of eminent domain takings under long-established jurisprudence: transfer from private ownership to public ownership and transfer from private ownership to privately owned public service (a utility is another example).
The third category is more recent and arguable: transfer from private to private ownership for public purpose. Before this ruling, it was justified by remedy to public harm (e.g., eliminating urban blight) but now it can be justified by increasing the tax base..
This third category shouldn't exist at all in my view (and that of Justice Thomas). It didn't become permissible until Supreme Court rulings in the 1960s and the 1980s ruled it permissible. Now it's been dramatically expanded..
A stadium is not a "public venue" in many cases. If the information posted here on FR yesterday about the ballpark in Texas is correct, then the Texas Rangers or their ownership is actually the owner of the facility.