To my best knowledge, in Shabbos Melochos we do not differentiate between גופו or כוחו, but if it it performed כדרכו (like it is intended to be used) or not (sometimes called בשינוי - literally "differently from intended" see Shinuy. The Hebrew version is much more detailed).
For example, if turning up the light normally requires a human finger, but you do it with a magnet, that would be שלא כדרכו and therefore fall (only) under a Rabbinical prohibition, just like turning it with a broom. However it it is intended to be moved with a magnet, that would be כדרכו and prohibited deOrayso.
THe differentiations you mentioned (גופו, כוחו, גרמא) are relevant to damages, not Shabbos, in that case the magnetic force is called כוחו (by his extended force) just like throwing a stone, but it does not matter to paying damages.
גרמא is all different story, relating to indirect consequences, not indirect force.