MSYS2 doesn't include mingw-get, it uses pacman instead.
From their website:
It features a package management system, Pacman, to provide easy installation of packages. It brings many powerful features such as dependency resolution and simple complete system upgrades, as well as straight-forward package building.
Pacman is much more powerful than mingw-get was. You should be able to install additional packages using Pacman instead of mingw-get.
MSYS2 was built around Pacman. So even if you could install mingw-get (like, manually downloading it and unpacking it, or rebuilding it from source), it's unlikely that it would do anything useful in an MSYS2 installation.
Adoption of Pacman also determine how the packages get built (through PKGBUILD files with the build rules), that's why MSYS2 is a rewrite of MSYS, where each package build has been remade from scratch. Pacman is so much at the core of MSYS2 that it's hard to detach them from each other.
(Perhaps a similar comparison can be drawn to Linux distributions. Can you install rpm on Debian, or dpkg on Fedora? Yes you can, but you most likely won't be able to use them to manage the packages installed on your distro, since the distro is built around the other package manager, which is at the core of that distro, in a way that's really hard to dissociate from it.)