At the risk of sounding like I'm just here to promote my own thing, you might be interested in my game Subtext. It's 90% automated, but otherwise it's fairly similar to what you're describing (I think).
Figuring out how to explain it to people is definitely a challenge you'll face with that sort of thing. I wouldn't shy away from calling it a game just because it's largely human-powered, although keep in mind that what you call it will somewhat dictate the audience you get and the way people view it. Sleep is Death calls itself a game, and reviewers mostly accepted that classification and talked about it in that context. By contrast, The Aluminum Cat mostly used words like "experience" and "adventure", positioning itself as more in line with immersive theater or tabletop gaming. Of course they're a little different since Sleep is Death was two player with one of the actual players acting as a game master, but my point is you can probably pick whichever angle you prefer.
The idea of leading in through a browser-based game sounds neat. You might get more people to play it if you prompted them to enter an email address, and then sent an email to them, rather than the other way around. From a software standpoint you'd ideally have something similar to a customer support system, where you'd be able to take notes that would be stored in the player's "file" and automatically displayed next to their messages so you could keep track of what was going on. You could also just manage that with a spreadsheet or something but (speaking from experience) you're going to want to simplify your workflow as much as possible and as fast as possible since dealing with that sort of bookkeeping gets old pretty fast.
Anyway, bottom line is it sounds cool and you should totally try it.