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.

You might be interested in some of the letter writing TRPG's that exist, they can easily be done as play by email. Here are a few I recommend and some info on them:

• PPVSS - Otherwise known as Pen Pals Vs Star Spawn. You and your colleagues have uncovered some hidden horror. Doesn't necessarily have to be eldritch, it could really be anything. This is a totally free game that can be played at about any pace you want. Unlike a lot of these types of games, it doesn't require a lot of investment and you don't need more than 2 people to fully enjoy it.
•  De Profundis Second Edition - Want a little more depth than the above option and don't mind shelling out a little cash for it? Then this game is the one for you. Personally, I would grab some ideas from PPVSS and toss them into this, but either way, the game here is very solid. The downside is that this requires a fair bit of investment and commitment as opposed to all the other options I will list here. Seriously, the game expects you to make this a lifelong pastime (you don't have to though, obviously). The coolest thing though is that the book itself is a wonderful piece of fiction, worth it for that alone if you ask me.
• By the General's Hand - Want something fairly light and only for two? Than By the General's Hand should suit you fine. There is a war, you and the other player are general's of opposing forces. It's very simple, but as a starting point it is solid. Game does cost, but it is really cheap. Not my favorite, but for the price and how easy it is to play, I can't really complain.
• Callisto - Finally I have saved the best for last! This is EXACTLY what you are looking for. It's a GM'ed letter writing game that folks can come in and out of. Any setting, as long as people need to communicate in some way, you can do it. Further more, it is strictly meant to be played via email as opposed to traditional letters, which cheapens the above games slightly. Edit - I forgot to mention this is PWYW, so free if you'd like.

I sincerely hope that one of these strikes your fancy. I am a big fan of interactive fiction games such as these. There are some solo games in this vein as well if you would like some suggestions on that front, just ask. Heck, even I made one! Anyway, even if you decide none of these are for you, I would very much enjoy hearing what games you end up looking into :)

Happy gaming!