What value does this provide? It looks like nothing more than a security vulnerability with a new non-standard and crippled interface. Tar is available on all the target platforms, for example.
I've run into it when I used to install Virtualbox "Guest Additions" or whenever I'd make the questionable decision to use the latest video drivers during my annual dalliance with desktop Linux a decade ago.
The value it provides is fewer steps in an installation guide for non-power users (or as jakobdabo mentions below, particularly for users coming from the Windows "double click to install" world). It would extract and run a post extract hook. I haven't come across it much in the last few years though.
(For installing non-executable material, it does elevate the risk.)
The thing is, that ship has largely sailed, with the proliferation of package management that prompts you for a password to go sudo.
sudo apt-get install whatever # trust your distro
sudo ./foo.run # trust foo.run's publisher, a bit worse
Just like Windows installers---which is why we need utilities like Revo Uninstaller. This lets us run the application's uninstaller first, then scan the entire filesystem and registry for what looks like bits and pieces that might belong to that program, and let the user select which of them to blow off. I use it quite a bit.
if the system has a tmpfs/ramdisk mount, it can also extract itself there, and have a no HDD deployment, which can dramatically speed things up too.