Top 3 in chess book sales are probably (not necessarily in order):
Everyman Chess
New In Chess
Batsford Chess
Next would probably be:
Dover Publications
Quality Chess
Gambit Publications
These are educated guesses, based on my 30 years of chess book collecting. While I cannot guarantee the allocation of the specific publishers in my two categories, I am reasonably confident that the publishers listed are the top 6 in sales (i.e., over the past 10 years, and presently), which of course implies that the top 3 are included.
"The rule of three in business and economics is a rule of thumb suggesting that there are always three major competitors in any free market within any one industry."
https://en.wikipedia.org/wiki/Rule_of_three_(economics)
Who are the top 3 for chess book publishers?