“OK, I think I get the concept. I've seen some forums where they have built-in random number generators for different purposes, but I didn't connect the dots to forum RPGs. As long as a GM is available enough to set difficulty levels for certain tasks, then that's one way to somewhat automate things. Of course, common tasks could have predetermined difficulty classes.”

Yup, I've seen this feature in phpBB3 too. However, it has some polish issues : the functionality is a bit hidden in the interface, and I have seen claims that the random generator is far from being perfect (as in 999 times one side and 1 time the other side for a 2-sided "coin" throw, which suggests some serious rounding issues). Nothing prevents people from deleting a post and re-posting it in order to re-roll the dice. And finally, I have some issues on a conceptual level : too much dice rolls tends to encourage one-liner roleplaying (especially in fights) and reduce the player's creativity, so I prefer to keep with strict storytelling for the most part, and it one day there's a need for stronger rules invent them at this point...

“You could also do away with DCs altogether using a system similar to FUDGE or the Vampire system you described.”

Actually, I think that both FUDGE and Vampire have something like difficulty classes. There's a score which you have to reach in order to success when doing something, which in FUDGE is reached through skill level + dice modifier and in Vampire or Shadowrun is reached by throwing as many dices as you have skill points and counting total dice score.

“One idea to implement this would be to have a "Roll Dice" tag, which when the post is submitted, would generate random number(s) for each tag placed in the post to determine success or failure, along with some special markup or some other mechanism to discourage shenanigans. ”

phpBB3 has this, but it's badly broken. Editing a post re-rolls the dices...