That sounds specific to using DNA tests for things like health insurance or work fitness. In most of the cases you don't need to swab DNA to find someone's race, sex or ancestry. You can find those by other means. So that law won't prohibit discrimination based on sex, race and ancestry.
I'm more getting at why value conciseness over clarity? Even if "genetic information" doesn't cover them presently, there's no reason it couldn't to achieve Gavin Newsom's new goal of not having laws be overly explicit.
If, as you have indicated, those provisions are already redundant under California law - of course I would. You seen to be asking this question as if you expect to catch someone in a contradiction, but I don't think you're going to find people support one situation but not the other.
Prior to this thread, I didn't really think folk would be up in arms in making the language of law being explicit in barring something we apparently all agree it does bar and should bar rather than leaving it ambiguous and reliant on judges not construing the law slightly less liberally than Newsom thinks they should. In other contexts, replacing the explicit callouts with ambiguous, broadly interpretable ones seems like the opportunity for harm is obvious.
The argument in the case of caste is that it's already covered by way of the law presently prohibiting discrimination based on "ancestry". But additionally, the law prohibits discrimination based on "genetic information", which seems like it would cover race, sex, and ancestry. Color, probably, too, unless that's intended to protect clowns and the sun tanned.
Edit: Similarly, would you say California erred back in 2005 when they amended the law to specifically include sexual orientation, as courts were already using the existing law to rule against sexual orientation (on the basis of it being also sex based discrimination, see like Rolon v. Kulwitzky back in 84)?