I don't get the scorn towards DirectX or Microsoft. Gaming performance in Windows compares well to other PCs, aka general purpose computers.
What AMD is attempting is extremely retro. Hardware and vendor specific APIs disappeared for good reason. You cannot compare a hardware agnostic API like DirectX to it.
DirectX, by nearly all accounts, is an excellent development platform. Like all platforms, it has strengths and weaknesses, but years of postmortems tell me it's generally well-liked among devs. It costs Microsoft money to produce, so I'm not sure why they should give it away.
Gaming performance on Linux is an extremely mixed bag and mostly unknown. There are not nearly enough titles available to properly judge. If you read about everything Valve has done to 'fix' Linux gaming the past couple of years, it's clear it was not a viable option for consumers or devs. How well they have improved it remains to be seen.
Can we expect Devs to learn two new consoles, adopt hardware specific APIs on the PC, and also begin supporting Linux at the same time? Good luck with that. Whatever change comes of these announcements, progress will be slow.
If mantle is gaining traction among Devs, you can bet nvidia knows about it and is preparing an answer. Devs are unlikely to support (which means more than initial development, but also testing and maintenance) dx11 + two different hardware APIs on the PC - so we might see an even more fragmented version of red and green team games. More fragmentation and frustration. And, perhaps worst of all, more confusion at a consumer level, further stagnating the PC gaming market.