Driving a manual car, rather than an automatic, teaches you nothing about cars, possibly bar the fact that they have gears. Even that is tenuous: the interaction between the clutch, stick and accelerator is a very abstracted interface to the actual drive mechanism of a car. Manually changing gear is just an extra dexterity skill to learn.
And the opinion is out of date.
The "learning x will make you a better programmer" argument has been made before. However, last time, x was Lisp. This makes sense, because in that case you're sacrificing performance to gain better tools to problem solve. But, in this article, the argument is that learning C++ teaches you about computing basics - memory allocation, storage, retrieval etc. But these things just aren't that relevant anymore. Problem solving tools are generally useful. Technical details are specifically useful, and thus less enriching.