I have always been a huge fan of crossword puzzles and, in a round-about way, my love of crossword puzzles was partly responsible for my decision to study linguistics in graduate school. So naturally, I tend to semantically analyze crossword puzzle clues while working a puzzle. As a result, I believe that the relationship between crossword puzzles and semantics should be seen as reciprocal because working a puzzle not only calls on semantic knowledge, it also reinforces and adds to a person's semantic knowledge, whether consciously or not.
The role semantic knowledge plays in solving a crossword should become clear by looking at some of the common crossword puzzle clue categories and the semantic concepts with which they can be compared.
Traditional dictionary definitions = reference
Thesaurus = synonymy
Encyclopedic = reference
Names = reference
Opposites = antonymy
Puns and wordplay = vagueness and ambiguity, polysemy
“A kind of” = hyponymy
Indirect = vagueness and ambiguity