Yeah the word "work" can be confused. What I meant by work was work where you are paid to do something for someone else. Maybe "job" is a better word. I don't have a job and I don't get paid but I do indeed still do a lot of work.
So does that resolve your confusion about the nature of vacation? :) Your statement "it's clearly not lack of work" should have been "it's clearly lack of job."
To me at least, vacation clearly is "lack of work" :)