If I try to select the Vulkan backend in Dolphin, then a window pops up saying: "Failed to create Vulkan instance" and the game will not play. But if I add the line "media-libs/mesa vulkan" to /etc/portage/package.use and remerge mesa, it works fine.
I'm not sure how this should be handled. Presumably the proprietary nvidia-drivers provide vulkan support. The vulkan-loader is going to load a driver, given whatever hardware is in your system. We could have a virtual/vulkan package, but I'm not really sold on the benefits of that. Not really sure.
Gentoo usually does not add optional runtime-only dependencies to packages. On top of that see Matt's comment on how to express dependency on vulkan in general.