the possessive "'s" only applies to animated possessors, living beings. "a word's gender" does not feel right. "the gender of a word", or "a word gender" should be the correct way, but the latter isn't accepted
I would normally say "the word's gender." "The gender of the word" also works, might sound better and be more correct, but takes longer to say. But "word gender" sounds strange. I'm a native of the US.