Depends what you mean by "default". Windows ships with DirectX, OpenGL and Vulkan support. Call of Duty runs on Vulkan by default, for instance.
Vulkan is notable as being new (doesn't have legacy baggage OpenGL and DirectX have), is natively cross-platform, and is often more performant than other options for modern games.
It's cross platform in that if you want, you can write implementations for other platforms. In addition to supporting multiple platforms in its current state.
The difference is that Microsoft is responsible for the DirectX API on Windows but does not have anything to do with shipping OpenGl or Vulkan for Windows.
Microsoft plays roughly the same role a Khronos (specifies the API, provide conformance test suite, provide an SDK, etc.) but when it comes to actually “shipping” DirectX, Microsoft doesn't have anything to do either, it's all on the graphic card vendor to ship DirectX drivers. As an example, for a while after its release, many people didn't have access to DX12 at all, just because their GPU didn't have DX12 drivers.
So the situation is much less different between DirectX and Vulkan than you make it sound.
Vulkan is notable as being new (doesn't have legacy baggage OpenGL and DirectX have), is natively cross-platform, and is often more performant than other options for modern games.