The first "writer's room" game I encountered (played it at an event) was Universalis (first release in 2002, very Forge Era). I pretty much described it that way before I heard the term (it feels like you are a bunch of writers brainstorming a movie or TV series.)
Most systems I've played along these lines seem like making sketches/outlines with the occasional fleshed out bit. You are not writing the full novel or reading the full script. You let your imagination fill in the gaps.
Many GMless games seem to fit this space, sometimes less explicitly than Universalis. I'd argue The Quiet Year does, and
Belonging Outside of Belonging engine seems to. My latest work,
God-Killer Prophecy feels like collaborating on an epic fantasy novel and I'd call it writers room (there is a prologue, three chapters in book one, three chapters in book 2, a final confrontation and an epilogue). Play rotates between a prophecy phase, which is a kind of chapter/world-region creation, and an adventure phase.
Todd has always called the
ScreenPlay engine writers room (ScreenPlay, High Plains Samurai) -- mostly I think this is in the "player's are encouraged to introduce NPCs." We didn't do that when I played a 1 hour demo of it though.
n.b. links are to Compose Dream Games Marketplace which I run. I get 15%, the rest goes to publishers. There is a UK site as well with many of the same titles.