Linux

Not specific to Mullvad, but you can use flatpak or your distro's package manager (probably apt) to install programs, On Ubuntu, you can open the software program and search the programs to install it, that should be the first thing to do when you want to install something rather than going to the website.

People here saying you can just download and run the .deb just like the .exe

Aren't you forgetting the "add +x permission" step?

In general, yes.

Your system has repositories with packages on its own, but on Ubuntu they're rarely up to date (which is ok, Ubuntu has older, well tested versions).

So what this guide does is it installs a custom repository which contains the Mullvad VPN packages (and some additional stuff needed to make it work, like the signing key for the packages). After you install the repository you can install the packages the way you're used to (apt, software center).

This has some security implications. The default repository is well tested and checked for malware and so on. By adding 3rd party repositories you lower the security because now the system can install from other, less tested sources (and it can, for example, create a package with the same name as some system library and with newer version - ensuring their version is installed because it's newer). It doesn't mean that using 3rd party repositories is bad, in fact I'd do the same if I had Ubuntu and wanted to install Mullvad, it just means that you should really check whether you trust whoever created the repository.

The reason why they're doing this instead of just giving you a .deb file to double click is updates - if you add their repository, the next time you update packages (through apt or update center), you'll update Mullvad as well, ensuring you're on the latest version. Because of that mechanism, software rarely contains code to check for new versions - on Windows you'd get some notification that a new version is available, here you'll get nothing because auto update through repositories is assumed (or it's executed automatically like for example Firefox does).

Someone already provided instructions on how to download the .deb file, so you can go that route, but IMO the better way is installing the repository (if you trust Mullvad).

Step by step

sudo curl -fsSLo /usr/share/keyrings/mullvad-keyring.asc https://repository.mullvad.net/deb/mullvad-keyring.asc - downloads their repository signing key into /usr/share/keyrings/mullvad-keyring.asc

echo "deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main" | sudo tee /etc/apt/sources.list.d/mullvad.list - creates a new file with the repository configuration in a location that apt expects

sudo apt update - after adding a repository, this command will download the information about all packages, versions and file locations so that apt install knows of their existence

sudo apt install mullvad-vpn - installs the Mullvad VPN itself

Hopefully I've cleared up things a bit, feel free to ask if something's unclear!