More people managers at a sufficiently high level. It's not that there are more managers than junior/mid/senior engineers, it's that there are more senior managers/directors than there are senior staff/principal engineers. At least at big tech companies, I understand that this is just true and by several multiples at that. So there would be several times more directors than principal engineers at Google, which are the two relevant roles at the same level (L8).

That's not what they're saying. At the lower and mid levels, there are far more ICs than managers. At the top levels, there are more managers than ICs (at each level.) This is the case in most major tech companies I've seen.