Yes, that also had me confused when you mentioned it.
mono Your.exe is actually a console command that alegedly can run the same executable produced for windows when on a linux environment with MonoGame installed. Haven’t tested that path yet. For now I can’t test much since I’m traveling for a couple of weeks, but probably I can build natively too with only the NET core embedded as you mentioned because I don’t like having too large dependencies to run this.
MonoGame is actually an implementation of the XNA framework made initially by Microsoft. It’s open source as well and has been my preference for a few years.