Had they argued that the Obama-era rules didn't apply to this case for some reason, I would've agreed with you. But the argument is that those rules should be overruled. That is precisely arguing that your preferred outcome for this case should be "extrapolated to wider society", as you put it.
If those two arguments would have been equally effective, then perhaps you would be right. I would bet that that wasn't the case, and that's why Google's attorneys advanced the argument they did. Perhaps you are right but they advanced both arguments to be safe, as a higher parent comment suggested.
But it's hard to tell, because the article is vague on these points. It refers to their actual argument only as "urged the National Labor Relations Board to undo that precedent". What exactly does that mean? It's written as if they submitted a policy brief, but it sounds more like they were arguing a prior decision by the NLRB was incorrectly decided, based on previous precedent. Which is something attorneys do all the time and much less dramatic, sans the lobbying-esque framing here.
