Not like in an official sense, but some guilds (especially social ones) do sometimes make up games or through guild hall parties. I have seen things like scavenger hunts (hiding a really small furnishing item ion an obscure place and offering a reward to the first person to find it and point it out, giving occasional clues if everyone seems stumped) and lawn darts (building scaffolding to climb up to a tall height in a house, then leap off and try to land your body on a custom-crafted target with a prize offered for hitting the target - that one it's preferable for whoever is running it to keep soul gems on-hand to rez the poor darts LOL).

That is basically how some groups or guilds approach role-playing, but there are limitations. Mainly you have to do it at a set time because the quest can only run when the people involved are online and able to play their parts, it won't show in the quest journal and of course there's no way to automatically award loot at the end - any rewards have to be mailed by one of the people running it.

But the basic idea is the same - a group of players is set a task which likely involves speaking to several other people (like quest NPCs, but they're players acting out the part), exploring a location somewhere and probably solving some sort of mystery or defeating a dangerous enemy. (Either they use a world boss or something as the quest boss or sometime do it via duelling.)

There's also lots of guilds who do less complicated activities like hide & seek, scavenger hunts and other 'mini game' type activities. Some are quick, others can go on for weeks with new clues being given out periodically.

Someone started an addon to do something like this. It is still in development: https://www.esoui.com/downloads/info2723-TheCompendiumDemo.html