To steam improve independence of distros, you should distribute steam at least in one extra form that is not package manager dependent, such as with http://icculus.org/mojosetup/
or a plain .tar.gz
The second part to improve this a LOT it would be a formal written permission to anyone repackage Steam for you own distribution. more about this here: http://steamcommunity.com/app/221410/discussions/7/846939071115939325/
Remove all "apt-get" related stuff from scripts. Unfortunately is pretty hard to guess package names for every distribution around.
All dependencies should be included in the package itself as its dependency, and in a form of a readme for the mojo setup version, or include as local library (then use LD_PRELOAD);
If while running you detect some missing package, you could give a dialog saying what is missing.
So, after that, the best would be if you create packages for all major distributions, so you could have more control of your environments.