Mantle came out in 2013 and there are exactly 10 games that support it, with no new games on the horizon. While Gameworks started in 2014, not including physx already has more than 10 games supporting various Gameworks elements, with more games on the way, and if we included all the physx games that have come out over the years, well, it would be a lot more. So no, Gameworks is doing quite nicely.
Known by who? Psychics? Because I can't find any articles to verify that claim.
If AMD's motives were purely altruistic, then why did they deny access to Intel or why did an AMD executive outright lie about there not being a new DirectX in the works? Why did AMD only open Mantle to the public after they had already completely stopped updating it?
Literally the only thing AMD "pushed" was Microsoft's annoucement of DirectX 12. Mantle was neither a sandbox nor a playground, it was a stripped down version of DX12(of which AMD had privy to since MS works directly with hardware vendors to ensure compatibility) that they rushed to release in a vain attempt to gain marketshare and only made good on their promise of making it open after the looming release of DX12 killed all developer interest in it.