and that the propellers are rotating clockwise?
The vast majority of North American built propeller aircraft have clockwise rotating engines, and I've never seen a specific reference to this in any other propeller or turbopropeller AFM / AOM for the other types I've flown. Not saying the reference is not there in other manuals, but this is just put down to general knowledge (in fact, this side of the pond we're often told the only people doing counter-clockwise propellers are the Russians).
But, to identify which way the propeller will turn doesn't require one to watch an engine start; just look at how the props are bolted onto the hub, as the position of the blade face (and, consequently, the blade back) will tell you immediately which way the propeller will turn.
who cares which engine is critical?
You're right that the average line pilot does not care. However, this knowledge is another tool in the toolbox that permits a pilot to know why they are "putting in more rudder input than would otherwise be expected." I've never subscribed to the idea that any knowledge is useless - who knows when you might just need to know that a certain engine is the critical engine? Better to know it than not.
Also, it helps to explain why some aircraft are constructed with a rudder that can travel a certain number of degrees further in one direction than the other.