TBH, WebGL does about 98% of what a 2D game engine needs, and WebGL 2 (which should be supported by a few browsers by the end of this year) makes it 100%. Also for games that are already GPU-bottlenecked (e.g. fillrate limits) changing the API will have no performance impact. So while I think Vulkan is a very positive thing for the industry in general, I'm not sure it will have much impact on Construct 2. I'm not sure there will even be a WebVulkan, but if there is I don't think there are many clear benefits to be gained relative to something like WebGL 2, and the downside would be having to rewrite of a lot of complex rendering code.
I think the most interesting possibility for Vulkan is that a browser starts using it as a backend for its WebGL implementation, which will more or less remove the graphics driver from the equation. This could provide much better reliability, and end problems like graphics driver blacklisting. For example Chrome uses ANGLE on Windows which is a wrapper library to convert OpenGL calls to DirectX - so the same mechanism could convert OpenGL calls to Vulkan and basically skip over a load of problems in drivers.