There is the LSB and the fact most distributions are based off one of the
bigger distributions. Since the cores remain the same there is usually no
reason you can't install from the distribution from which your distribution
is derived.
For instance Trisquel and Linux Mint users can install any packages from
Ubuntu and there generally shouldn't be a problem.
I would classify most games under three systems:
Generic installs: This installer will work on any version of GNU/Linux, and
should install and operate under any conditions. This version is the only
version that can be installed completely in a user account.
The RPM version: This is used on distributions such as Red Hat, SUSE, and
Mandriva, that use the RPM package management system.
The DEB version: This version will operate only on Debian distributions of
Linux such as Ubuntu.
There may be a few variations of this like different versions for 64 and 32
bit systems.
The real issue to supporting multiple distributions comes down to there not
being a system in place to collect donations, raise funds, or otherwise
provide monies to the developers to live off. A lot of projects are not
terribly well funded and survive off the existence of large corporations.
These corporations may not really care all that much about any particular
distribution.
Ideally there would be more people working on developing start ups with free
software compatible business models and working with non-profit projects to
raise funds. A few successful projects survive this way. I won't name any as
the large ones I can think of off the top of my head aren't completely free-
although I am thinking of ones which are included in Trisquel and have
probably less than a dozen lines of code which have changed.
