E.g. a company that uses people to calculate taxes is not tech, whereas a company that uses people and software to calculate taxes is a tech company if their use of internally-developed software gives them a significant competitive advantage over other companies in that market.
EDIT: Thinking about it a little bit more, a vegetable growing company is not a tech company unless they use software to drive down expenses so they can compete better, allowing their investment in software to give them a greater rate of return than a comparable investment in additional people/other capital. Typically the automation system is also licensed for sale externally at sub-linear marginal cost. This means that tech companies benefit from a faster rate of growth than a traditional capital-intensive business, while driving up productivity in their market.
WeWork probably qualifies then. With sufficient scale they could bring technology to bear in order to increase utilization of office space. Especially to global companies that have ever changing needs for office space around the world.
Of course, WeWork hasn't (AFAICT) accomplished that but theoretically they could.
That growth will eventually level off.
The definition you provided included this bit about "(thereby scaling non-linearly)". If actual growth does not matter and the only criteria are marginal cost reduction and automation that requires software, then why mention "scaling".
"Tech" companies are like pyramid schemes.^1 Unless there is growth, the "business" does not "work". This might have something to do with the fact that most of these companies do not generate enough revenue to survive, and rely on investment rounds to pay peoples' salaries.
1. Every participant had to recruit six new participants for the scheme to see any return from their own investment.
"Tech" companies are not self-sustaining, they cannot draw the requisite investment to survive, without "non-linear" growth.
There’s also an implication that they will scale faster than linearly.
Personally, I like working for business where actual technology is the differentiating feature, though they don’t always succeed. But money is hardly my main motivator.