Read the paragraphs directly before: Engels refers to “arguments as these”, so we can safely assume that the example he gives there is representative. What’s his example? Safety in railway operations.
That, indeed, is not a job for a delegate, a person chosen by council to represent the council in a bigger council, a political position which comes with no authority, but one of a safety commissioner, a person who was entrusted with, granted authority, by a council to enact necessary safety procedures for the common good. The railway safety commissioner would be choosen by the railway workers. Someone they trust to be a stickler to details and procedure.
Both, btw, are recallable on the spot should they abuse their positions, or turn out to not be suitable for other reasons.
This is not a mere “changing of names”, the tasks are completely different in character and the levels of authority could not be any more different. What Engels seems to be incapable of conceiving is that an e.g. city council doesn’t have authority over a neighbourhood council. That the delegates the neighbourhood councils choose come together in a city council and then precisely not dictate to the neighbourhood councils what they’re supposed to do. That’s your brain on hierarchy.
So, yes, Engels concludes that he’s right. And thereby proves that he either a) didn’t understand what the anti-auths were telling him or b) didn’t care, as authoritarians are prone to do when challenged on the necessity of there being rulers.
As to “labour cannot be organised without hierarchy” in general: It’s long been proven false. There’s a gazillion of examples in which it has done. There are, right now, armies out there operating without hierarchy that are fighting both Cartels and ISIS, very successfully so. If armies can be organised like that, surely it does work for ice cream factories. Stick to materialism, please, your idealist claim doesn’t become true by repeating it.