This is a useless definition, especially in this context. Washing my dishes is not work, because it's ultimately irrelevant whether I do it or not, although I'm doing it still because I have a result in mind.

It also comes across as very out of touch and privileged, because unless you have a relatively cushy job, you would definitely not see the difference between being paid or not as irrelevant. There are plenty of people who have to work very hard just to make ends meet, be it physically exhausting work, or repetitive and monotonous work. And they will not have the capacity to work even harder once they clock out of work, no matter the incentives, because they'll be spent and unable to.