This is utterly ridiculous. I think it's generally understood that, in the 21st century, a "tech company" is a company that uses tech as the principal competitive advantage to replace traditional "non-21st-century-tech" incumbents. Obviously, Netflix used streaming, collaborative filtering recommendations, and a massive CDN to replace cable TV subscriptions. If that's not a perfect example of a tech company, I don't…
Then Disney, HBO, and CBS are now tech companies.
To stretch your analogy, you might even argue that Target and Walmart are tech companies too. Or UPS, DHL, and FedEx. They do massive scale logistics using computers.
I would go by a different definition for tech. Are engineers the principal innovators and expense driving the company forward? Are automation, growth, measurement, iteration, and hard problems a chief mindset? That's what tech is to me. You could even meet those definitions without being an internet company. SpaceX, Tesla...