I have not played or GM'ed this one yet; this review is entirely based on reading the rules and listening to RPPR's actual play (Bouncy Castle Inverness!)
The Play's The Thing is a game about actors playing characters to put on a stage play. So you, the player, are an actor who is, in turn, a character within a play. You the player are in-character as your actor who can yell 'cut!' to try and talk the GM-who-is-the-play-director into allowing an edit to the play as y'all rehearse. Actors have types, plays have places, and characters have parts, plots, and props. Got it? Good, 'cause I need another read through of the rules or three.
One of the things I really appreciate the author doing is the nine Shakespeare plays they broke down into a cast list and five act structure that fits the rules set-up. One, that's like including nine one-shot adventures just ready to go for new GMs. Two, it's a great illustration of how to do it for any other play. While the central expectation of the system is that you're going to use Shakespeare's plays, I honestly don't see why you couldn't use a play from someone else. It's a nice flexibility to the system that I appreciate.
From the rules, this system also appears to have hit a sweet spot a lot of indie narrativist games have a hard time finding, the balance between doing a type of RPG play really well and long-term play. The system deals with the problem of character progression leading to over powered character really fast (*cough*Monster Hearts*cough*) by making progression non-linear. You don't get better at bending the story in your direction, you change up your approach and goals by shifting between actor types. It's character development instead of skill development in a way that allows the player to write a narrative for the actor over several sessions who writes narratives for their part in each session.
Admittedly, I'm not sure how many non-theater nerds are going to want to play a campaign, but I think the structure in the rules is there for it.
I'm looking forward to trying this out with my gaming group. I'm thinking of trying to adapt The Maltese Falcon to the system as a play and seeing how badly the plot gets butchered :D