If you define organisms that use the energy of motion to create food as kinetitrophic organisms, then the process could be called kinetisynthesis.
So we are talking about hypothetical organisms and making words up. Welcome to my world.
If you go into a cave with flowing water, or any underground pipe, you will find organisms living attached to the substrate, but in complete darkness. Are they heterotrophic or autotrophic? You know they are not phototrophic because there is no light.
When we were in school, we learned the “formula” for photosynthesis:
If we go to school long enough, and take advanced biology courses, we find out that this formula is oversimplified.
Oxygen is a waste product for photosynthesis. Complex organic chemicals cannot be made without sources of carbon and hydrogen. And if those sources are water and carbon dioxide, the inevitable result is that oxygen is generated.
The final product does not have to be sugar. Try it with a formula for lipids or proteins. Try it with the Hover and Porges formula for bacteria:
When you balance it out (and you might want to try ammonia for the source of N), true autotrophic organisms that use carbon dioxide for the carbon source and water for the hydrogen source must generate oxygen.
Chemotrophic autotrophs typically rely on the oxidation of an inorganic compound, so they use oxygen as a part of the reaction. But kinetitrophic autotrophs, if they exist, would likely generate oxygen as a waste product. Unless, of course, they build their bodies with chemicals other than carbon dioxide and water.