I looked up the show This Is Our Youth that was on Broadway last year, and it was the first time it has been on Broadway. So why exactly was it nominated for Best Revival of a Play at the 69th Tony Awards?
Read the Tony Awards bylines. It's the same reason why Hedwig and the Angry Inch was considered under the Revival category. It doesn't necessarily have to have been on Broadway, but to see a production on Broadway of a show that's already relatively known in New York will usually constitute a revival rather than an original production. Again, the specifics are in the bylines themselves
"A play or musical that is determined by the Tony Awards Administration Committee (in its sole discretion) to be a 'classic' or in the historical or popular repertoire shall not be eligible for an Award in the Best Play or Best Musical category but may be eligible in the appropriate Best Revival category, if any, provided it meets all other eligibility requirements set forth in these Rules."
Although never previously on Broadway, THIS IS OUR YOUTH was considered by the Tony Committee to be "in the historical or popular repertoire."
All the other responses are correct, but as I've said on this board before, one of the most simple ways to think about it is this: if it's the production is a revival of an already-existing work, then it will be considered a revival. Whether or not it's been on Broadway before is essentially irrelevant. The same was true for all of these shows:
Oh I see. Thanks everyone. I never really considered the fact that those shows including TIOY are considered for an award because they were all previously shown in New York at some point in history. Including Off-Broadway. I always believed that the Tony Awards were specifically for Broadway Theater only.