Rumi (the Sufi mystic) apparently walked and turned in circles in order to contemplate. The tradition merges music and movement with philosophy and religious mysticism.
Walking, dancing or manual labor (for example gardening or cleaning) can all be done in a meditative way.
But these are likely different types of meditation that have different effects. Even just a calm, sitting meditations might be vastly different from another, depending on the meditation object.
Of course there are people who lean into specific types over the others as you describe, but I think many of these activities share a common core and experience.
I buy it. I'm not really into meditation, but am deep thinking/reflection.
I found I got by far the most intense deep thinking sessions while mowing the lawn with a push mower. It was a large-ish yard, took around an hour. It's boring, monotonous, requires no thought. Keeps your hands occupied so you won't be tempted to 'check something real quick'. And lastly, loud enough to block any other sounds that could make your mind drift(sirens, birds, dogs barking, etc).