Sure, but that team may have N engineers and those VPs may have N teams, so that doesn't seem so ludicrous for a 7000 person company. Or even 3500 person company by EOD. Certainly in my company there's about a 200:1 engineer:VP engineering ratio, so pointing out every engineer reports to a VP is kind of a meaningless statement
And there are also finance people, HR people, sales, etc. people. The company is far from entirely engineers, their managers, and the managers of their managers.
> There seem to be 10 people "managing" for every one person coding
Take this literally, not as as a ration. - each SWE in a product team has an EM, Dir Eng, VP Eng, PM, Director Product, VP Product, ...