It means that some level of knowledge (i.e. knowing how to do something) is required to perform the task.
How much knowledge? Several different levels, depending on the context.
An adjective can help clarify:
"A cursory knowledge of ___ is required to ___."
"An intimate knowledge of ___ is required to ___."
Used without an adjective, it would be dependent on context to tell how much knowledge is required.
In this case, "A knowledge of the rules is essential for all chess players" would mean that anyone who plays chess would need to know the rules. "A knowledge of game trees is essential for all chess players" would imply that good chess players should have a fairly deep level of knowledge about the potential outcomes of a given move. (I certainly don't have that knowledge! Of course, that's why I'm not a chess player. )
In my opinion it means that even a small knowledge is required to chess players.
Because when it says "improving chess players" means that you don't need to be very good in chess..so it speaks about beginners chess players.
Chess players only need to know how the pieces on the board move. But chess players who want to improve need to know the playing techniques associated with open and semi-open files. (Whatever those may be.)