Japanese Play-by-Postcard RPGs: Net Games (2017)
dampfkraft.com
dampfkraft.com
We managed to play once.. this year.
Unfortunately it also feels like, to do it right would require it to charge significant fees. There would be a lot of effort required reading, collating, adjudicating and responding to each and every player even if groups doing roughly the same thing got shared replies. Probably more than an individual game-runner with a hobby could do.
I think MUSHs fit all of those except asynchronous, but I think there might be asynchronous ones out there.
It wasn’t as difficult to manage as I think many assumed, although mandating that the game must go on even if people missed something was tough sometimes.
Each school day we would bring the disk with our turn and hand it in to him and he would hand back our disk from the previous turn. It was a blast and great fun given the limitations of tech at the time.
Pages 70 & 71 of "Signal: communication tools for the information age" (A Whole Earth Catalog) have details.
I'll take a photo and put it up on Imgur, because the official site is broken.
Here's a link, sorry for the poor photography: https://imgur.com/a/4miM4vP
This and the OP's example might actually be closer to a form of literature, but one that is semi-interactive and non-linear. I've been keeping a list of digital examples of this [2] but perhaps I should start an offline list, too!
They claim to have been running for 20 years.
Maybe not exactly for yourself, but maybe doing it for your kids and involving them could be something.
"Celebrities" have backed them, they come in life, fantasy, sci-fi, business, crime, sports and every other genre you can imagine.