If they are working at a company then they are working class.
If your wealth derives primarily from your labor, you are in the working class.
If your wealth derives primarily from your wealth, you are in the ownership class.
Do you have an alternative definition?
Both views have their merits. A software engineer and a nanny both sell their labor... on the other hand, the fact that the former can employ the latter and the reverse is not true suggests their position is not entirely the same.
If you insist on reducing all of us to only two classes, then working vs owning is one way to do it... but not the only way. One could also divide the "paying" class from the "charity" class, for instance.
And a software engineer at Microsoft with a 401k and a portfolio of stock grants has one foot in the ownership class, even if they still work.
General observation: Anyone who says "there are only two X..." is trying to make you view the world in reductionist terms, and they're choosing the terms to make you focus on the issue that they want you to focus on. But the world has a lot more nuance than that, and some of the other nuances also matter.
Capitalists have capital.
The rest of us are born with only our labor to sell, whether that labor is blue collar or white collar.
The middle class is was and always has been a lie to separate the working class.
I put my best effort into waking up for bullshit 6am scrum meetings with my global team a few times a week, eventually with the constant stress of some bug being discovered and having to hold for the next sprint and dreading 1-on-1s with this asshole manager who'd consume the entire time with me having to justify why I "wasn't coding faster"; eventually getting laid off during the worst downturn in the tech job market I've ever seen.
People move between income sources...
I don't know Zuckerberg's biography but I'd wager to say he didn't have to work or starve ever in his life. And I'm no Bhaskar Sunkara but I'd also wager to say >50% of zuckerbergs wealth is due to the surplus labor value his employees create, not his labor. So in a material examination of Zuckerberg you'd say indeed the issue is not the phase of his life where he worked for a living, but the phase where he is extracts maximum surplus labor value from his workers. That phase constitutes X-99.9% of his wealth, so he is not exactly some hard to pin down edge case
This isn't to say that any company that derives a profit is an evil exploitation factory, it's just an idiots understanding of a useful jumping off point for material analysis.