So by that logic if Uber ever does migrate completely to a self-driving taxi system, it is no longer a tech company.

That seems fair to say. If Uber transitions to self-driving taxis the whole business model will be radically different. They'll have to employ hordes of mechanics, and lease huge garages to store vehicles and run repair bays. They'll have massive capital expenses, a complex supply chain to manage, and a large distributed and probably unionized workforce to negotiate with. Their geographic distribution, legal exposure, exposure to economic shifts like tariffs, reliance on capital markets, number of employees, etc... will all be radically different. It seems fairly obvious to say that pre-self-driving and hypothetical post-self-driving Uber are totally different kinds of companies.

Uber’s primary business is finding and exploiting legal loopholes, and ignoring regulators. They happen to have an app, that’s all.

An analogy would be a pizza company where you order a pizza with an app but it actually gets made in some random person’s house.