No it wasn’t, it used the same (albeit highly modified) engine, if that makes HL a mod then almost every game you play is a mod since they all use some preexisting engine. Otherwise you have to consider Marvel vs Capcom infinity a mod of Daylight since they’re both UE4 games, or even Call of Duty as a Quake mod.

You don’t need Quake to run Half-life, therefore it’s not a mod, it just uses the same engine, or some parts of. That is very different from Counter-Strike which you needed to have Half-life and mod it to be able to play it originally.