This actually belongs in tech support, where there are threads aplenty about people trying to install NS into a Steam account which doesn't have HL Classic (The GoldSrc version, not the Source version) assigned, and installed in it.
However, to save you looking, every thread has the following in it.
"I can't install NS on my Steam. I've got (Insert one of the following) Half-Life Source/HL2/CS/CS:CZ/CS:S/DOD/DOD:S installed, so why can't I install this?!"
"You need Half-Life 1 in your account, bound, installed, and played at least once."
"OMG WHY NOT WHAT I'VE ALREADY GOT"
"Please, read the installation guide"
They're the general giste of how the threads go. Natural Selection was designed with the GoldSrc engine in mind, specifically the one that comes with Half-Life, mainly because it uses some of the same files as Half-Life does. There
is a way of getting it to run on CS:CZ, but it's unsupported as of about 3.0. No-one in the community (to my knowledge) uses anything later than 3.0 on a CS:CZ install, without Half-Life. So that method is pretty much dead as they come.
Congrats on finding the forums though