The error actually tells you exactly what the problem is. You either don't have Vulkan compatible hardware, Vulkan compatible drivers, or you need to update the version of Vulkan (usually packed with your drivers, but not always) as there's a mismatch. You can have a higher version than the game, but the game can not have a higher version than you. Since you're actually getting this error, I'm under the assumption that that means there's no OpenGL version, so unless you can fix your Vulkan problems, you wont be able to run the game.
Looking over the mess of Vulkan errors you have, its not seeing your graphics card capabilities which is telling me its one of the first 2. If it was you having a lower versoin of Vulkan than the game, you'd still be getting 1s in most of those checks instead of 0s. See if you can find an OpenGL wrapper for Vulkan. Vulkan was made by the same guys that make OpenGL so something might have already been made.
Edit: this was made in Unity3D, there's no way that it doesn't have OpenGL support unless they hard coded rendering calls in, or Unity3D itself removed OpenGL. Try searching for Unity3D runtime arguments to force OpenGL mode, I know they exist because I've used them for Kerbal Space Program (try -opengl)
Edit 2: the correct argument is -force-glcore taken directly from unity's manual