DXVK is an API designed for Linux. It actually works with WINE; as for Windows, it's more or less experimental. Not all games perform better in fact some might work the same as if you were using DirectX under Windows.
There is no way to see if you're using DXVK under Windows though, since DxDiag only reports DirectX versions. It can't detect Vulkan, you would in theory need a third party program and even then, it might not show your game's running state.
DXVK works if you see a sudden performance boost in game, you don't need an app for that the difference is clear and apparent. Some games however require the dx
.dll to be (renamed) replaced completely, as they might have a file structure that is hardcoded into the exe.
There may even be a possibility the game you are running or trying to run doesn't use DirectX to begin with, in which case DXVK won't work at all.