Some people can play chess blindfolded. There is a popular method of memorizing which has one visualize the placement of objects in a familiar space. Both of these seem absurd to me, as I can at best conjure a fleeting glimpse of an object in greyscale. When I calculate chess tactics I do so in a manner which seems almost kinesthetic, as if I’m feeling the movements of the pieces, and I have to look at the board while I do it. When I memorize things, like poems or the digits of pi, I just repeat them until each element of the sequence magically evokes the next. There is no visualization.
Those two example skills are probably unrelated, like two aspects of the same what-are-your-brain-interconnects problem.
I can place symbols and move them, but I can't imagine a realistic flower; if I tried hard enough I could memorize a chess boards, but the pieces wouldn't have exact shapes as such, everything would be just a representation of a thing, not comparable to a visual memory of seeing the layout. In programmer speak, I think in nodes, graphs, connections. I can imagine people moving in a room to great detail, but not at all their faces or clothing.
I'm strongly spatial but not photographic at all. You're probably strongly tactile, and you learn a poem as if it was muscle memory of a movement.
No, that is muscle memory. If I play the piano with my eyes closed, I'm not visualising the piano, I'm focusing on the feel and positions of my fingers
This is my experience as well. I would also say that when improvising I’m not really thinking consciously about the movements, but rather the notes I want to hear.