I wish nVidia could bring out it's own API, but that would mean that either nVidia keeps it's promise from September and releases hardware info like AMD and Intel do, which they won't, or that the Free Software Foundation accepts what is basically a Trojan horse into GCC (the GNU C Compiler, the foundation of everything that basically works as advertised on this planet), which is a huge danger to open source, and which is the solution nVidia is trying first as a potential cop-out on their earlier promise. If the first happens, that would mean that nVidia would need to start making serious products and drop the "Apple" attitude, products that don't use cheap tricks, products that are standard compliant and actually work as advertised, which would force them to compete on price and features with Intel and AMD, which they want to avoid at all cost. If the second happens, they will always have to deal with a compatibility layer between the Trojan Horse in (mainly the OpenACC part of) GCC and their actual PTX assembler, the proprietary language that drives the nVidia cards that is non-standards-compliant and has a limited functionality, which means that the nVidia cards will lose a lot of performance there.
nVidia couldn't implement Mantle, the cards are not compatible enough for that, nVidia would have to make structural changes to it's hardware designs and start making more expensive cards, which would have to compete with cheaper competitive designs, so they are not going to do that.
Mantle cost AMD nothing, it's just a small part of a toolkit they have been developing for about two years. The benefit is that Mantle can break the DirectX hegemony, and that's exactly what AMD and Intel (Intel graphics hardware could probably use Mantle without much problems, Intel has chosen a very similar design path as AMD, they just have a hell of a lot to catch up, but Intel has never ever developed anything so fast in it's history as the Ivy/haswell/broadwell open source iGPU linux drivers, and AMD has actually pretty much stopped Catalyst development to support open source linux driver development, because all Intel drivers are open source and AMD wants to catch up with that. Mantle is not the final goal, I'm sure that OpenCL/OpenGL/OpenMP are the final goals, because a few fps more in games is not the final goal, hybrid system architecture computing is, but AMD and Intel have to get rid of Microsoft's technology blockade to realize that goal, because Windows really can't make that transition in an efficient way. First step is to win the youth, the next generation consumers, and that is done with games and stupid irrelevant benchmark marketing, because that's just the way it is, so Mantle is a good instrument to pry open the cracks in DirectX, which would bring game devs over to Khronos Standard compliant code, which would make the final goal possible.
The performance benefit of applications running in linux with AMD APP optimisations, Mantle's "big brother", the full HSA API, is exponentially greater than AMD APP optimisation for Windows. That proves the point of Mantle being a pry bar. Right now, games that run OpenGL already look a lot better than games running DirectX, the textures are clearer, the lighting is more natural, the blooming effect is much more restraint and not as obnoxious as on DirectX, and the fps is better. AMD and Intel both want scalable systems, that are completely usable with iGPU solutions for gaming, and DirectX and Windows now make that impossible. An Acer C720 CrOS-book for instance is a typical example of where the industry wants to go: cheap, but thanks to linux still very good performance, and a lot of practicality. Useless on Windows, very useful on linux (CrOS or more serious linux distros). At the same time, people are getting true HPC performance with relatively cheap scaled systems, for example with linux miners on the consumer level, something that is also impossible in Windows. In universities, scaled APU+multi-GP-GPU systems in small form factors and with small power requirements, are being used as portable HPC systems. That was never before possible. Intel wants a part of that with iGPU and Phi cards, AMD already has the hardware ready to go with GCN cards and APUs. AMD and Intel have both ends of the budget spectrum pretty much covered in the next-gen HSA hardware. They seem to have found their respective market targets without annoying each other too much. Intel can make third-party solutions, AMD can't, AMD sells Intel products, Intel catches up with AMD's HSA strategy... they seem to have reach a mutually beneficial truce. Both of them control the x86 platform, and whatever nVidia does, it will have to accept the direction Intel and AMD set for the x86 platform. nVidia keeps selling stupid hot air functionality for a very premium price as long as they are in the game, basically as long as consumer computing is hampered by the Microsoft technology blockade: G-sync, which makes no sense in linux because the problems are solved at the base, in other words, G-sync solves a problem that doesn't really exist in linux, H.264 encoding, which is a 2003 standard, completely ancient and proprietary, and solves a problem that linux doesn't have, because en/decoding in linux can perfectly be done efficiently without taxing the system to the point of performance loss (through OpenCL, etc...), CUDA, which lacks the instruction compatibility to even start to compete with OpenCL, which requires a different hardware approach than nVidia is using, etc...
Mantle will deal with DirectX. The thing that Windows is now still holding onto is the deal Microsoft has with Adobe to boycott open source platforms. As everybody knows, some Adone applications run faster in wine than in native windows, but still Adobe won't release linux versions of it's creative suite, and that's not all, Adobe has also stopped developing the linux flash client, and have frozen the linux version to one that uses an absurd amount of CPU, to the point that running a flash youtube video, makes an i7 Haswell laptop throttle because of overheating. They can easily solve this, but they won't, which implies bad faith (they do provide better flash players for some linux distros, Android for instance). HTML5 works fine, but is being boycotted as long as the open source world won't accept a DRM-mechanism being embedded into HTML5. I do hope that it never happens at all, and that eventually, people just stop implementing flash, like a lot of websites already have. Apple has done a lot of pioneer work there, by not supporting flash on their mobile products. Of course this has made Microsoft very protective of flash, and Google is playing a vicious role in flash support, and some stupid websites only work with flash, like twitch.tv, googlevideo (youtube with advertisements), etc... so there is still a lot of work to be done there, but eventually, the technology blockade will fall apart, and take Windows and probably Microsoft, Adobe and nVidia down with it. Microsoft is virtually bankrupt, and that's a fact, because of this:
http://www.fosspatents.com/2013/12/federal-patent-court-of-germany.html
Which is a confirmation of an earlier 2007 verdict, and basically means that the FAT-patent of Microsoft is ex tunc null and void, which means that all the license fees Microsoft has gotten from Android manufacturers and other victims, could never have been due, so have to be paid back with interest. In the EU, consumer class action cases are also facilitated by the legislation, so a lot of people are now joining an initiative to ask their 10 EUR on their Android phone back from Microsoft, and if Microsoft would have to repair the damage done to industries and consumers in the EU alone because of it's null and void patent, it would already go bankrupt, and banks would also reconsider the asset value of Microsoft because the FAT-patent goes from one of their biggest assets to one of their biggest liabilities. Ballmer insisted on stepping back before the court ruling came out, and has probably covered his arse in this matter, because obviously, declaring a liability an asset is a crime, and although the patent isn't declared null and void in the US yet, it's highly probable that the US will not be able to maintain a conflicting legal position, because that would mean that the US would not have access to some of the most wanted and sold technology. Microsoft will probably be buying a Qualcomm-manager to succeed Ballmer, so they are clearly aiming at dumping their x86-focus, which means that Mantle might already have given the required effect.
Another point is that a services company can tailor-make a linux cocktail for specific consumer targeting, like SteamOS or CrOS, or smart TV's or Android... that is also impossible on Windows, which is so heavy that the threshold for hardware products that can easily sell the services, is too high. A Steambox with Windows would be futile, because the performance would not compete for the price with consoles. Linux makes it perfectly possible to get really high performance out of very cheap systems. If games are developed with the D3D API, the transition to linux can't happen, so Mantle is a transitional technology to convince developers to use Khronos spec API's, which is basically what Mantle is.