AMD want Mantle to be mainstream, by mainstream i mean widely used and fully compatible with Nvidia and Intel, for AMD its not about getting one over on the competition, perhaps to their competitive detriment it never is, with the exception of 64Bit computing they have never made any of their technology proprietary. 3D Shadowing, Dynamic Global Illumination, TressFX and 'in development partnership with Hynix' GDDR5 to name a few; are shared with Nvidia.
The thing is right now the OGL PS4 is significantly more powerful than the DX11.2 XB1, people know this and its getting slaughtered in the sales by it.
Microsoft need to respond fast, and cheaply, AMD hold the key to that, which puts them in a dictatorial position, what AMD can say to Microsoft is "Mantle in DX12 in its entirety on the Desktop or your on your own"
Which isn't actually a bad thing for MS to go along with, that would create 100% parity with the XB1 and the Desktop, Developers will love that and for Microsoft it puts one over on the PS4 as it would be the odd one out in development terms. Win Win Win.
Incidentally DX11.2 (available in Win 8.1) was also developed in partnership with AMD for the GCN based XB1 with the understanding that it would be available on the Desktop.