Would it not be just the coolest thing if GOG set up a fairly quick computer and established a GOG server that we could all play on?

Hahaha it would be interesting, but I'm not sure how it would work with Darkstone!

After one beats the game what happens? Everyone gets to wander an empty world?

Maybe I just don't understand what you mean by doing that, but it's not quite the same as things like Battlefield or an MMO afaik :)

Once you beat the game, it starts over with new levels and an increased difficulty.

It'd be awesome for a place to share and trade gear and adventure together. But suddenly I see your point. Level 1 dude shows up in a world that's been beaten 6 times and he might find himself dead pretty quick.

I would have thought you'd need to manually get it to start (and I know this, I'm on Hero difficulty atm haha). Not sure if you could get a computer to automatically rehost (either on the same difficulty or a higher one), but if that's possible it could work (e.g. Mondays are Novice, Tuesdays are Expert, etc).

Also I'm not sure how many people can join the same game? It could get awfully crowded (players block projectiles and some spells, AND DOORWAYS -_-; haha) and hence messy :P