Installing programs on Linux without root privilages
It's quite easy to install a program without root privilages. What Steam does is it just drops the binaries in your home folder where you have read and write rights, and optionally it can create a .desktop file in your home folder so it appears in your application list in the GUI. If we installed games in $PATH they would have to have been binaries which is a pretty big jump from how games are stored now. Now that I think of it, it's probably not the most difficult thing ever to put an entire game inside of a binary, including existing games, look at Appimages for example. Flatpak and GNU Guix (Not sure about SNAPS, I not very familiar with them) use similar tricks, they also install everything to the home folder. What you could do is add a folder in your home directory to $PATH and then you are free to drop files in it which can then be called like normal programs via the command line. Distros like Fedora are by default configured to look for binaries in ~/.bin, so you could drop any kind of executable in this location and run it via the command line by calling it's filename.