Linux Gaming

GNOME doesn't really care about shortcuts on the actual desktop, but you could put those gamename.desktop shortcuts Steam created into ~/.local/share/applications instead, and then they will appear alongside your Applications in GNOME.

~ represents your home directory, basically an alias for /home/username/ so you wouldn't have to type that in a terminal all the time. .local/ is a hidden folder (that's what the dot at the start does) and you might need to check if your file browser is showing hidden files and folders to see it.

To get more in-depth help in the future, you should probably state what Linux distro (Ubuntu, Fedora, Arch...) you are using too, different distros can have different ways of doing things!