I'm not a fan of Stargate builds personally, they have to do damage to really break even since the tech is pretty dead-ended in comparison to things like TC, and most importantly, they're harass and not pressure. So long as Z secures their third and gets a few spores over there, they're fine, and what they're doing in the meantime is making pure drones because you've guaranteed your actual army count isn't going to be high for awhile. Still a viable style though.
You might be confusing stargate opening and dedicated stargate build. While opening is harassive and buys you time to tech to robo or mass gates, stargate build gets mommaship and voids to grab very safe 3rd, and harass is a mere option, not a liability. And while zerg is droning, I'm chronoing probes. By the time my 3rd goes down (min 9, when mommaship pops), Zerg is usually ahead by at most 10 drones, given he pulled off a fast 3-rd. Then it becomes a matter of efficient army trade and containing zerg on 3 bases.
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