Perhaps the question of whether or not Assassins should be considered a "new" musical or a revival hinges upon who the producers are.
Case in point: The recent production of Metamorphises originated in Chicago, and was subsequently produced in both Seattle and Los Angeles before moving to off-Broadway. After considerable success OB, it transferred to Broadway, and I believe won the Tony for Best Play, or was at least nominated. All through the extended period prior to Broadway, it kept the same basic production team and cast. It was the original production, and therefor a "new" play.
Case in point: On the other hand, Little Shop of Horrors was originally produced off Broadway, and has subsequently had numerous productions across the country and the world (plus a film version). The current production is NOT the work of the original production team, nor does it include the original cast. It therefor should be considered a revival.
I understand that Weidman has done some revisions to the book, and Sondheim loves to tinker with things he's written before. However, the Broadway staging of Assassins does not involve the original producers, designers or cast. It has had major productions in several cities, and in some cases more than one per city. It is no longer the original work. It is thus a revival.