Where did you get the package? Are you following some install instructions somewhere? If so, which ones?
I've downloaded it from the official steampowered.com site and tried to install it with a double click, after that i've tried to install it with
sudo gdebi steam_latest.deb
Like it was discribed here: https://wiki.ubuntu.com/Valve
Have you tried the other suggestions on that page, such as using dpkg?
Yup, both.
The installed Version of Mint, was a fresh installation with all updates, it could be, that the problem is fixed, because i've heard of some people that doesn't have any problem with the installation.
http://steamcommunity.com/app/221410/discussions/0/828939163741016475/
Meanwhile i've installed Mint 14 again. So i can't test it.
Okay recently i've installed Olivia again an now it worked like charm. No problems so far.
Possibly just a corrupt download then, is this closeable as it cannot reproduce?
Nothing extracted yet.
Today i've installed the Release Candidate of Linux Mint 15 (Olivia).
After that i've tried to install steam, but i've encountered the following error:
Could not open steam_latest.deb
The package might be corrupted or you are not allowed to open it.