Valve ported Source (and with it LFD2, Half Life 2, etc.) to OpenGL + Linux and got big improvements in speed. It was about +15% without any driver optimisation at all.
The next thing they say is openGL with more fps is doing frames faster... well from the quote maybe I'm missing it, same game same OS different renderer, who knows. openGL and DX will perform differently in different games, same as most OS's and most hardware. There will almost certainly be games where openGL has a lower framerate and a higher frametime... the average frametime is completely useless in talking about how smooth something is.
As for openGL, it should have been pushed more and it's entirely down to MS pushing DX for donkeys years. There was a time though that DX got REALLY pushed while openGL dropped back in features at which point dev's went with the "newer" features and API and never really had a reason to switch back as both gpu makers prioritised DX driver support also.
Fact is most engines already do support multiple API's and adding more adds more work... but that isn't an issue, that is part of making an engine. For DICE to make an engine that is compatible with more computers, more platforms and more gamers..... they are increasing the amount of places they can release a game, what will support it, all for minimal cost.
You spend 2 years coming up with an engine, the next decade tweaking it and updating it, the 3 months to add brilliant support for a new API which enables all those games they and everyone who licences their engines to more platforms and more customers... it's a no brainer.
SteamOS most people are presuming(almost certainly correctly) will be all games supporting openGL, with multiple/most crossplatform games having an openGL rendering path already, the only thing to add is a little platform specific testing. More cost, yes, potentially reaching more customers... price/profit argument and clearly the idea is winning.
Ultimately MS is about rehashing code and doing things messily and cheaply, they have been for years. The ridiculous install size of Windows vs any other OS is... insane. It's bloated, buggy, security hole ridden mess and every dev has basically agreed for donkeys years that DX isn't anywhere near where it should be.
If every game dev today dropped dx, didn't do a second more work on it and only went with openGL, most games would work(or be made to work pretty easily) on most platforms, windows included.
In terms of Mantle and the xbox, in almost all likelyhood it is on Xbox, it's likely on PS4 and it's almost certainly AMD software that they've let MS use, not the other way around.
Otherwise we're talking about MS writing an API then allowing AMD when asked to release it on PC's which would help push the market away from DX and the windows lock in. The chance of MS doing that is essentially nil, I'll be shocked if that's what happened. With the similarity of console/amd hardware, it would be basically a waste for anyone but AMD to have written it then given it to MS/Sony to add their own individual tweaks to it to take advantage of their particular hardware.
One huge advantage to Mantle is currently it's designed for gaming, it's from a gpu maker and being targetted via game dev's requirements. DX is controlled by MS, but they get input, and openGL is controlled by a ridiculously large group of people who get to have their say. DX has an advantage in the one voice one direction, quicker changes(if MS were quick and were sensible that is). openGL changes need to be approved by a huge number of companies and people, extensions don't get full support, it's not really set up to be a gaming only standard which I think limits how fast it can move.
openGL is to me almost too widely supported/used/targeted, too many people involved. Mantle has the advantage of being new, ground up, efficient(most likely, I'm guessing here) heavily targeted at current gen equipment to help leverage that power better, with a very limited scope of gaming, with only one real voice to say yes/no to changes, it can move quickly, adapt and they are really only interested in what game dev's need/want and they can push both hardware and the API towards the same goal very quickly.