While many industries have an element of zero-sum competition, that's not the default. Whether you're designing a car, doing a surgery, giving a haircut, cooking a hamburger, etc. you are giving something of value to your customers.
You’re describing retail jobs, where that might be true. But most white-collar workers never interact directly with customers. They have to demonstrate value to their boss, which does make it a zero-sum situation.
I don't think any of the jobs I listed are retail. I went out of my way to include a variety of industries, including knowledge work. "Demonstrating value to your boss" could include zero-sum bullshit or actual production. As a programmer, I've done both kinds of work.
Even assuming (optimistically) that an exceptionally good hair stylist could somehow... uh, I don't know, be so good that they can hire more stylists? Assuming there's space?... it's pretty rare to have, say, multiple heads of the same department.
You could cut more people's hair by getting it done faster, or do a better job cutting each person's hair. The point is that jobs where productivity improvement is possible are very common. Economically, productivity and technology are equivalent, and are the basis for prosperity. Productivity is not, in general, zero-sum.
The post uses accounting, which, well, maybe it's a different story if we're talking about complicated tax schemes that can save a lot of money, but in general I think we can say that if the workers are more productive fewer rather than more are needed.
It seems to me like this claim contradicts your previous assertion that there's "no zero-sum game." The zero-sum game is, they only need so many workers, and if all your coworkers are achieving levels of productivity only possible with chemical enhancement, then you get left behind.