I don’t know about Mac, but on Windows the Mullvad app doesn’t auto update. If you want to do it Windows style you can look for deb files (which are like installers) or AppImages (which are like standalone executables).
Most pieces of software give terminal instructions for Linux because different people might use different package manager frontends, but literally every Linux user has a terminal. It might seem daunting at first, but giving users commands to run in their terminal is a lot more simple than trying to walk them through repo management through the GUI, or just telling them to figure it out themselves.
The instructions on that page make it so that every time you run a system update, mullvad automatically updates as well. If you’re happy doing the updating yourself, you can download the deb file from here: github.com/mullvad/mullvadvpn-app/releases