Hi Margherita,
I'd like to call your attention to something interesting on the video. Please look at the opening of the piece, specifically measures 5 through 8, heard during seconds 10-13 on your video. Here both hands are simultaneously playing the same figuration in parallel. Neither hand has any advantage over the other as they are simply mirroring one another at the separation of an octave. It would be similar to playing the C minor scale hands together in four octaves ascending and descending in parallel motion. The principles and articulation are the same for both hands.
Now, during the execution in those measures, watch closely the wrists of both hands. Your right wrist is a wonderful example of how this figuration should be played. Notice how your forearm, wrist and hand are neutrally and naturally extended to the keyboard. In fact, you could even lay a ruler over those three links in the playing apparatus, and the ruler would be as level as a perfect highway. Nor is your right wrist rigid despite appearances. It is only as supple as it needs to be.
Next watch the left wrist in that same section. The left wrist is undulating up and down like a porpoise swimming in the sea! So in the same figuration, the left wrist motion is altogether different from the right wrist. If the music were requiring you to drop the LH into a chord, and there was then a slight drop of the wrist as a follow-through motion, it would be explainable; or, if the LH were lifting to taper off the end of a phrase, that motion would be justified too--both of those being just a couple of examples of flexible, vertical motion in the wrist.
From watching, I get the same sense as birba, that is that the left hand thumb is a bit "lazy" and not fully articulating. Thus, because it's not articulating, and yet you must play the piece, the wrist is over-compensating actively trying to counteract the relative inactivity of the thumb. The wrist and hand are wonderful at positioning fingers, but are no match at all for the actual dexterity of the fingers. While the wrist is doing everything it can to adjust for the thumb, it can't fully succeed in that task--because the task is impossible. In fact, it sometimes causes the execution to falter, producing unevenly played notes, notes that are too quiet, missed notes or even wrong notes.
Perhaps try this: Forget the right hand for the time being. On those measures I mentioned above, play the left hand alone. In doing so, your intent is to replicate what the right wrist can do automatically. So, extend the LH naturally and neutrally to the keyboard. As you play the figuration, you do NOT want the LH wrist to be like a door hinge; rather, see if you can maintain that straight line of the forearm, wrist and hand requiring more of a firm wrist during the playing. But the whole mechanism is not tense, but rather relaxed. Then play as slowly as you need to, and gradually bring it more up to speed. Immediately the thumb will be obliged to actively assume its role and to play its notes. If you succeed, I believe that you could then transfer that same technique to the rest of the piece. Bear in mind that this cannot be corrected overnight. It will take some time.
So why does this show up? Because this is a left hand etude! Oh yes, the right hand plays melodic octaves and adds much drama to the music. But the left hand does most of the work while the right hand gets most of the glory. That's one of the benefits of the Chopin Etudes--they test the fine points of technique and help to improve it. But they're also beautiful pieces to play.
I hope this helps.

David