PS4 doesn't use OpenGL. I don't know why everyone thinks this, but it's not true and never was.

EDIT: the developers of The Crew talk about the PS4 API's in this article, if anyone is interested.

I'm sure most PC games won't bother with it, but probably at least a few high-profile games.

Modern OpenGL and D3D almost exactly the same extractions and pipelines, and for the most part expose the same exact level of functionality and performance (Nvidia's extensions for bindless textures and bindless multi draw indirect would probably be the most notable exception). Most of the differences between the two are completely superficial and stylistic in nature. I have no clue what would make you think that D3D is "designed for people who don't have the time to learn the nitty gritty of what state blocks, vertex, and pixel shaders do", considering that "state blocks" considering that you literally can't draw anything at all in modern D3D without using state blocks and shaders.

DirectX is "proprietary" in the sense that MS created it and is solely responsible for making new version, but legally-speaking it's not actually exclusive to Microsoft. Anyone else can implement that same API (or parts of it) if they have sufficient motivation to do so. For instance Valve uses an "implementation" of D3D that they use on Linux, where the D3D calls are implemented using OpenGL.

Since XB1's GPU uses GCN architecture it's highly likely that most of Mantle could be made to work with its GPU, but there's not really much point in doing this outside of making porting easier for a game that already uses Mantle. If it were to happen it would be on MS to make it happen, and I don't see why they would spend time and money on it. The version of DirectX that they use on XB1 probably already provides low-level access to the hardware. That was definitely the case on the 360, where the API resembled D3D9 at a high level (and you could treat it as such if you wanted to make porting easier), but it provided extra layers of low-level access that were specifically tailored to its GPU. The same goes for OpenGL: MS could implement it if they wanted to, but there's no reason outside of making porting easier.

OpenGL is available on Mac/Windows/Linux PC's, and mobile phones/tablets. The only time its showed up on consoles was PS3 which had a stripped-down version of OpenGL available to make porting easier. However most games didn't use it, and uses the low-level API instead. PS4 has its own custom API that's tailored to the hardware.

I don't know if they've announced platforms and hardware for Mantle yet. Windows is a given, but Linux seems like a possibility as well (especially if Steam Boxes become popular). It's built around GCN, so it's probably only going to work on 7700/7800/7900-series cards, Sea Islands 8000 series cards, and the new Rx 200 line that was just announced. I very much doubt that it will show up on PS4, since they have their own API.

85K is still a lot of triangles. 150k was probably excessive.

It has a full hardware encoder, it doesn't require any compute resources. That diagram is demonstrating that parts of it are programmable if you wanted to do a hybrid solution, which could let you use customized algorithms and/or encode faster than 60fps. There's a brief overview in this article.

Not unless you consider a tablet controller to be a "big leap".

I still call it GGD, so I would support this.

Just an FYI, all GCN-based GPU's have a hardware H.264 encoder that can handle 1080p at 60fps.

While the Thief franchise isn't exactly a household, it was decently popular back in the day and had a strong following of fans. They probably figure that the remains of this following will help hype up other games by talking about how much they liked the old games, and how they would want to play the new one.