> If I person is going to spend an hour building a stadium, they will not be creating anything else with that hour or engaging in valuable leisure time.
This is just talking about opportunity cost then, not the Parable of the Broken Window.
> If we pay (or tell/force) people to build a stadium - regardless of who pays (the owner, the public, a Genie) those people will have to NOT do whatever else they might have done.
Yes, there are opportunity costs to the things we do. But this applies to anything, not just new stadiums. If you choose to buy a new computer or travel for a vacation or install a new toilet you could have been doing something else with that money. The key here is that in market economies (this is everybody, US, Norway, Japan, wherever) people are independent agents and can allocate their time and resources how they see fit.
There is a different, unrelated theory of similar/same name which might be what you were thinking of. https://en.wikipedia.org/wiki/Broken_windows_theory (this isn't what I was talking about)
"I don't think building a new stadium is analogous to breaking a window." It is, in the sense that building a stadium or repairing a window both require forgoing something else that could have been done instead.
"...it's not a mutually exclusive endeavor." It is most certainly mutually exclusive. If I person is going to spend an hour building a stadium, they will not be creating anything else with that hour or engaging in valuable leisure time.
If we pay (or tell/force) people to build a stadium - regardless of who pays (the owner, the public, a Genie) those people will have to NOT do whatever else they might have done.