I never said "normal activity," I said other physical activity. Exercise is a subset of all physical activity, done to improve fitness, build muscle, etc. Although I suppose mental activity burns a lot of calories too, so perhaps I was too restrictive in only saying physical activity. I didn't even consider other caloric sinks, like wound healing or low ambient temperature.
Anyway, exercise becomes work if you are getting paid to exercise, but it remains exercise in either case. Obviously.
All that is exercise obviously, as well as his job, like you say. "Normal activity" seems to be your thing. Lots of things can be normal activities for someone and not normal for another person. I imagine exercising is a normal activity for Usain Bolt and Michael Phelps, so it would be both.
Running to catch an elevator isn't exercise, for instance. You're not running to improve your endurance or become faster at running or more fit, you're just trying to catch the elevator. My friend who runs miles upon miles every week because her hobby is running in marathons: that's all exercise, because she is running to improve her endurance. But it's not something she gets paid to do, so it's not work.
I never said he should. It was an example of how you said one thing when you apparently mean something entirely different. To be clear: a construction worker wouldn't need to exercise at all to lose weight, nor does anyone else. Reducing calories is sufficient. There's no need for a huge caloric deficit to lose weight without exercise.
"Normal activity" is your thing, so I won't touch that. The delineation between exercise and all other physical activity is, as you say, if you're just doing it to burn calories, build muscle, etc., it's exercise. Everything else is not. Work is something you get paid to do, and it may be exercise, some other physical activity, or something else entirely.
Sure, you could call it anything, but you will facilitate understanding if you describe things accurately. I could call all rectangles squares in math class, but if I had to explain every time that what I mean by "square" is "squares or rectangles," it seems strange to not just call them rectangles to eliminate the confusion.