I installed Steam on Debian 7 (64bit) and got steam to install (with a custom installer) boot and download games. I tried booting both Dota2 and CSS and both lock on the loading screen.
do you have the proprietary drivers for your video card?
Games are 32-bit, you'll need the 32-bit libs for graphics, and for some games the 32-bit libs for sound also, but mostly just graphics.
Yes I do.
I installed ia32-libs and also ran dpkg --add-architecture i386 to install 32bit packages.
Than add yourself to the group "video" and that should get you sorted.