To my recollection, none of the MSG venues have ever been a member of the Broadway League (and thus eligible for Tony nominations).
This isn't a show that needed an out-of-town. It's the Rockettes. They are a New York institution. They come with a built-in audience. What they were trying to do was come up with a Summer show for the Rockettes. This way they don't have to wait an entire year for the lucrative Holiday season. They wanted a show for the summer tourist season.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle