Aye, Valve's 'Source 2' engine already has Vulkan support firmly established though as mentioned currently the only public showing of that is the DOTA 2 transition to the Source 2 engine that happened a while back... can't say I've really heard anything in regards to DX12 support in Source 2 but I'd be very surprised if there was any given Valves stance in regards to Microsoft and the direction they're taking Windows.
Unreal Engine 4 already offers Vulkan support to developers using the engine to build projects utilising Vulkan right now.
Unity I think has Vulkan support due in the next month or so (well they stated Q3 2016, but with Unity things often get pushed back and happen several major build releases later than announced).
And Crytek have confirmed CryEngine will offer Vulkan support but don't recall a estimated timeline on that.... knowing CryTek it could be tomorrow or sometime in 2030 either way you know it'll be poorly documented.
In terms of those 3 packaged engines, I can see Vulkan getting a fair of utilisation over DirectX 12 simply because it will be alot easier for the companies developing those engines to offer more consistent performance levels to developers making use of their engines without laying on the additional burden of making sure custom shaders and the like working with one platform build can sanely be translated over to builds for other platforms given that easier multi-platform build compilation is one of the biggest draw factors for such engines beyond the obvious removal of needing to write your own engine from the ground up.
But the important thing will be what developers that do opt to develop their own engines gravitate toward, and a big factor in that will be how consistent driver support is for one API versus another across the likes of AMD, Nvidia and.... *shudders* Intel.
The following is a entirely fictional example but to illustrate what I mean....
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If Nvidia for example decided they're lagging behind AMD in optimised Vulkan support driver wise but notice AMD offering slightly less return in optimised DX12 driver support, Nvidia might decide to play into that and focus driver optimisation more heavily toward DX12 and less performance return with Vulkan.
As Nvidia are the 'Go to' company for most consumers looking for GPUs with some swearing blind that they will only ever touch Nvidia GPUs as 'they are best', if Nvidia driver support for Vulkan undermines developers efforts to utilise Vulkan cleanly by making it harder for them to provide consistent performance on Nvidia GPUs, then you'd almost certainly see developers shift to focusing on DX12 simply because it makes their life less complicated and stops all their players grabbing pitchforks and holding them to blame when their titles don't run solidly on their "20GB Titan 1337z0r edition".
(And this isn't to say this is a Nvidia-specific behaviour. AMD doing the opposite could equally be another potential example to illustrate the same hypothetical scenario)
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It may sound silly that any company would do that and that the end result could be like above, rather than people actually getting clued in and going "Hang on... no. They're just trying to be <bleep>ers and it's not the developers at fault there".... but it happens, and people are much more likely to blame the developers than their machine purchases. Especially if they have experiences playing something running on an entirely different engine utilising completely different APIs, without issues.
They're probably equally unlikely to even consider the possibility that the title has fallen prey to an businesses efforts to try to redirect the industry in a way that suits their interests by strong arming developer efforts in a favourable direction.
*looks at this thread*