Uber is definitely a tech company. They have internal software infrastructure that would rival any other, and attract similar talent as other tech companies. American Airlines is probably as much a tech company as Walmart is...
Yeah. You're absolutely right. I suppose working in "tech" is probably a more powerful distinction than working at a "tech company". For instance, if you work on the data science side of a political campaign, it's probably fair to say that you work in "tech".