No, they are managers; management and leadership are different things. Being a manager is a set of things that a person is authorized to do on behalf on their employer, "hire, command work and fire" as you said being examples. Leaders nurture their staff so that they work together effectively as a team to achieve goals. Very few managers are good leaders.
I saw (a black & white hand-drawn version of) this image [0] a while back and found it a really effective visual to easily explain the difference between a boss and a leader. (Here's an article that expounds on the topic and has some variants of the preceding image. [1]) I've worked with/for both types and the first type (boss) simply does not inspire loyalty or any interest in "going above and beyond" the bare minimum of absolutely required work from their employees.
The genuine leader type on the other hand often didn't even have to ask employees to put in any extra effort toward their job. Folks just generally went out of their way to try very hard to do their very best work (or damned close to it) for the true leader-type because it wasn't uncommon to see the "leader" right there "in the trenches" with them "getting his hands dirty doin' the work" right alongside them, and it just didn't feel right to not put forth at least the same effort he was.
I think (at least to my mind) the difference (in employee attitudes) is one of respect (leader) vs fear (boss).
Having had to estimate peak user traffic patterns, bandwidth usage, etc. for continent-scale services, Fermi estimation questions (https://en.wikipedia.org/wiki/Fermi_problem) are excellent questions for people working at the largest scales. Even if the guessed inputs or formula for the estimate are imperfect, being able to bang out an approximate formula that can brought out for discussion with peers and refined into something that can be agreed upon as a target is extremely valuable. It's not a useful skill for everyone but for those aspiring to be more than a mere coder, it's worth knowing.
