The docstring of `kill-matching-lines' already says (just at the end):

  If you merely want to delete the lines, without adding them to
  the kill ring, the M-x flush-lines command is faster.

True. What's missing there is the name correspondence/similarity.
I think it would be more helpful if it used `M-x delete-matching-lines'.
Following that link, a user would see that the other name for that is `flush-lines'.

but the one for `delete-matching-lines'/`flush-lines' does not mention the kill- version.

Yup. Wouldn't hurt. No reason to copy to `kill-ring' if that's not really what you want. And some users might not realize the difference.