First of all, I believe the rule is that the theatre has to be in Manhattan, not that it has to be in the theatre district specifically - happy to be corrected if I'm wrong.
And with that in mind, secondly:
Having 500+ seats and being in Manhattan are not the "definition" of a Broadway theatre - they are some of the required qualifications to become a Broadway theatre. It's a subtle but important distinction, because there are several theatres that meet these qualifications, but are not Broadway theatres. This is simply because the people who run those theatres (like City Center, Radio City, The Armory, The Apollo, New Victory etc.) have decided that they do not want to operate as Broadway theatres.
The "definition" of a Broadway theatre is simply a theatre that operates under Broadway-specific contracts, in addition to meeting the physical requirement, and "registering" with the Broadway League to be included as a Broadway theatre (I'm not sure if "registering" is exactly the right word to describe the process, but I believe it conveys the basic concept of what happens when a theatre becomes a Broadway theatre)
Hope that helps answer your question. And of course, to those reading, I'm happy to be corrected on any of this if anything I said is inaccurate - I'm certainly not the biggest expert on this board on topics likes this.
Updated On: 10/2/20 at 12:46 AM