Then I'm afraid you have Counter Strike: Zero, not Counter Strike 1.6.
The only way you can download Half-Life through Steam is if you have the original Counter Strike. And if you can't download Half-Life you can't play ESF.
Pretty much all you can do is pick up a cheap version of Half-Life, that's all the advice I can give you.
Edit: And please don't double post, I appreciate you want to play ESF but it's against the rules here. The advice you want is
here and
here but it won't tell you anything I haven't already.