I'm not sure why this is especially more dangerous than ordinary Linux packages provided by distros, let alone games installed by means other than Steam. A game is an executable, running any executable with your privileges provides access to your home directory. That is ordinary design for a Linux program. What is the home directory for, anyway? Again, it is absolutely normal for ordinary programs including multiplayer games to use the network.
Connect your PCs to the internet through a firewall and don't install Steam on production servers.
The point being: right now distro provided packages are screened and vetted, as are steam games. Moving away from that model has obvious security implications.
Connect your PCs to the internet through a firewall and don't install Steam on production servers.