It is rather interesting that it is more often interpreted as a national characteristic - something uniquely Scandinavian - than a characteristic of the lower classes, which was the intention of the author.
As somebody from the UK it's strange that I find a certain source of solace from this kind of culture even though practically it doesn't seem to make sense to dislike those who are succesful.
Except even in this case, others must be aware of the person getting things done. If you managed to do a lot of work and people literally didn't notice or attributed the work to someone else, you won't be respected by them. So what ends up earning the most respect is the ability to spread knowing of your accomplishments without appearing like you are boasting about your accomplishments. That said, in such a system the people likely think they are valuing the person quietly getting things done, ignorant of what they actually value.
As someone who have lived in a few countries and visited many more, I think the law of jante is a description of the social dynamics of scandinavian societies much more than of anywhere else (Denmark much more than Sweden)
There are other dynamics with somewhat similar results - a French friend told me that 10 years ago, starting your own company in France was the thing you did after you failed to get a job delivering the mail - leading to very little entrepreneurship - though he said it is changing in the last 5 years.
I have visited them and indeed I find a certain split between my experience of people's cultures and values say in the south of france and italy than I do in germany or russia.
I'm not sure if I really want to make the conjecture that there are two kinds of societies but I feel that on this issue it would certainly seem that way.