I think you're making a good point. A lot of people reserve the word "mindfulness" for the sort of meditations you're describing here and use "meditation" for something more specific. But they're just names and I don't worry about them too much.

This all also reminds me that there are people who view "true yoga" as a sort of 24/7 meditation of movement, where the person strives to be aware of and deliberate about their movements all the time.