What version Linux are you using and are you seeing any errors?
Make sure to install the vulkan drivers for your distribution of Linux.
https://linuxconfig.org/install-and-test-vulkan-on-linux
And also the utils with:
sudo apt -y install vulkan-utils
However, bear in mind that chromebooks are generally not very powerful and you may have performance issues when running the game.
I had a quick google of that error message and it looks like your GPU may not support vulkan.
Here's the list of vulkan conformant devices on Kronos' site: https://www.khronos.org/conformance/adopters/conformant-products