Eh, I’m not so sure about the Forges influence. I think it’s more that some folks who have influenced game design hung out there. It may be a subtle difference but I think it’s an important one.
One of the most influential RPG frameworks at present is PbtA. That was written by Vincent Baker. If you read the acknowledgements in the rulebook, you will see this (on p 287-88):
IMMEDIATE GAME INFLUENCES
3:16, Gregor Hutton
Ars Magica, Lion Rampant
Bacchanal, Paul Czege
The Burning Wheel, Luke Crane
The Mountain Witch, Timothy Kleinert
Mouse Guard, Luke Crane
Primetime Adventures, Matt Wilson
Shadow of Yesterday, Clinton R. Nixon
Sorcerer; Sorcerer’s Soul; Sex & Sorcery, Ron Edwards
Spione, Ron Edwards
Talislanta, Bard Games
Trollbabe, Ron Edwards
XXXXtreme Street Luge, Ben Lehman
Character moves are based on secrets in The Shadow of Yesterday, by Clinton R. Nixon. Highlighted stats work very
much like keys in the same.
Highlighted stats also follow fan mail in Primetime Adventures, by Matt Wilson.
Hx is based on trust in The Mountain Witch, by Timothy Kleinart.
Stakes questions are based on stakes in Trollbabe, by Ron Edwards.
Threat countdowns are based on bangs in Sorcerer, by Ron Edwards.
Holding creation (et al) is based on covenant creation in Ars Magica (2nd Edition), by Lion Rampant.
The character sex moves were inspired by Sex & Sorcerer, by Ron Edwards.
The character playbooks were inspired by XXXXtreme Street Luge, by Ben Lehman.
“Tell them the possible consequences and ask” and “offer an opportunity, with or without a cost” are based partly on “Taxi Service on Al Amarja” by Jonathan Tweet.
The entire game design follows from “Narrativism: Story Now” by Ron Edwards.
I think the Forge has been
extremely influential in RPG design.