In theory, every session would be one particular job. The GM chooses how many franchise dice need to be earned to complete the job. The core mechanic is using small dice pools for conflict resolution/did you actually do it using six-sided dice with the high roll being the one that counts. On a five or six, you earn franchise dice.
Okay, let's talk about what actually makes InSpectres interesting. One of the driving forces behind Sorenson's goal design was to create a system where missing clues wouldn't drive the game off the rails. How did he do that? By having the players add clues and have some narrative control!
If a player succeeds, they get to narrate the success. Which doesn't just mean explaining how they hit a mummy with a folding chair but the results of things like research or gathering equipment. That gives them a lot of control steering where the story goes.
But the really interesting mechanic is the confession camera. Once per scene, one character can step through the fourth wall and give a confession camera monologue. Which can include talking about events that haven't even happened yet!
Back in 2002, this mechanic would have confused me all to heck. But by now, even I know what a confession camera is, which means probably everyone else in the world does too. It's a wacky mechanic that I've never seen anywhere else but, at least today, is one people would have no problems understanding.
InSpectres was one the earlier games that broke up the narrative structure of RPGs, although it wasn't the first. I'm pretty sure Trollbabe came out before it. Ars Magica had the option for troupe play. Baron Munchassen was already out.
Frankly, not only do I have no idea what game first gave players control over the greater narrative, I bet you could find examples from the 70s. I've found that many Indie ideas have seeds from the roots of RPGs, seeds that just needed refinement.
I have no idea what I would have thought of InSpectres if I had played in back in 2002. At the time, I was firmly entrenched in traditional RPGs with D&D being my main focus. (Come to think of it, since I'm in a D&D campaign on Roll20, it's back to being my main focus :D) It would have been very strange to me.
But, having played a bunch of Indie games now, including some with no GMs, InSpectres seems really accessible to me now. It comes closer to the traditional RPG structure than even some of its contemporaries like Trollbabe. Even the confession camera rule uses an idea that is now firmly a part of pop culture. This would be a great game to introduce people to non-traditional RPGs or even RPGs period.
More than that, given its light-hearted feel (seriously, you don't have confession cameras in dark, serious games) and minimal setup requirements (since the players help write the story as it goes along), InSpectres would be great for a casual summer campaign. Since the game is about the franchise, missing players would just be on other jobs and you could even rotate GMs.
I don't know when I'll next be in a position to be in a campaign. But InSpectres is definitely on the list of games I'd like to try as a campaign.