What computer and OS do you have that can't run docker? You can run a full stack of services on a random windows laptop as easily as a dedicated server.
That doesn't make any sense to me. It can be installed directly from pacman. It may be something silly like adding docker to your user group. Have you done something like below for docker?
I thought it would. If it still requires sudo to run it is probably just docker wanting your user account added to the docker group. If the "docker" group doesn't exist you can safely create it.
You will likely need to log out and log back in for the system to recognize the new group permissions.