Your reply is entirely reasonable but it seems the gp already covered what you wrote and anticipated it in his disclaimer: ">It needn’t be employment,[...]"

He just happened to use the imprecise label "work" -- which is so tainted and overloaded that one can't re-use that word to also describe "non-employment intellectual activity" because it inadvertently tricks people into talking past each other.

(E.g. Notice that you used "work" as synonym for "employment" but the gp did not.)