Most people are not Feynman. Most engineers today think they have the capability of being Feynman one day - of course, statistics dictates that most will not be.
This is why Feynman's advice is powerful -
The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to.
Feynman here is instructing someone with too much ego, not too little. Koichi Mano thinks the problems he's working on are beneath him - that he should already be working on Feynman level problems! This is why he writes with shame to Feynman about his "humble" problem. Feynman demonstrates to him that no, no problem is too small, and backs it up with how he chipped away at "lesser" problems for a long time to build up confidence and competence. Finally, he closes with advice that could be ported to a middle manager at the smallest bureaucratic company who thinks they don't do anything important -
You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office.
If you do not have too lofty of an opinion of yourself (less ego, not more), then you will not be ashamed of the problems you succeed in, and only then might you have the chance to do something important.