When there is some real external test of skill, it isn't painful to be at the bottom of the hierarchy. A rookie on a football team doesn't resent the skill of the veteran; he hopes to be like him one day and is happy to have the chance to learn from him. The veteran may in turn feel a sense of noblesse oblige. And most importantly, their status depends on how well they do against opponents, not on whether they can push the other down.
It is nice to be in a group where people can do praise-worthy things and be praised for them. And, as the conclusion addresses, it is nice to give praise when due. This norm can be eroded by braggers. But it can also be eroded by people taking any mention of an accomplishment as a slight.
For example, the Oxford anecdote seems like the author going out of his way to feel slighted and assume malice. The excited salesperson anecdote is similar. Do others have a duty to mask excitement out of worry that it could be interpreted as bragging?
One of the best habits I have adopted is muttering "good on them" and moving along when an emotion suspiciously similar to jealously starts bubbling up.