OMG! @carbe, your wrist is ultra-stiff!!!
It's a pity because I see you have some talent and your rendition of fantasie-impromptu could sound nice but this will not happen while you still have your wrist completely immobile, accumulating tons of tension. Be careful, your actual technique is prone to create a serious injure.
Playing only with fingers is never the best way to play piano (wich must to be played with the whole body). But it can work apparently well with pieces written for other instruments such as harpsichord or not very complex classical and romantic pieces. Anyway, although we could believe it works more or less fine with this kind of repertoire, it's still a mirage, it's not a good technique, also not for these pieces.
But it's in a piece like Fantasie-impromptu where the futility of playing only with the fingers manifests crudely. Otherwise, playing with the help of the wrist and the natural weight of the arm and the body does not only helps to play more relaxed, releasing tension and economizing muscle resources, it also helps to obtain a better, rounded, richer, musical sound.
But the movement of the wrist is not an arbitrary one. Like the bow of a violinist, the wrist of the pianist helps to draw the melodic line (of course, there's much more than this).
My advice is that you must start as soon as possible with a good teacher who have a good technique. A forum can help but, in my opinion, changing one's technique as you need immediately, is a task only a teacher can do.