I tried installing a game but EA app doesn't install. It is quite a fresh install, it works fine on my other computer. I should add other steam games launch fine without the EA app dependency.
Have you activated the extra repository (Arch) or Chaotic-AUR ?
https://wiki.artixlinux.org/Main/Repositories#Arch_repositories
https://aur.chaotic.cx/
After that :
pacman -Ss steam