Take a look at the action of your right leg. It kicks off to the right. Instead, your right foot should kick toward the back fence (not the side fence). Will Hamilton of FYB talks about this in his serve progression. You should be able to see it in the serve motion of nearly all modern elite servers.
Also notice the direction that your left foot is pointing on your ad-side serves (in your 1st link) when you land. It is pointing way off to the left. Notice that Maria, in the image above, gets well into the court when she lands and her left foot is pointing, more or less, in the direction of her serve. With your right leg kicking off to the right and your left foot landing off to the left, you are often falling off to the left. Your leg drive should be up and forward -- you should be falling in the direction of your serve, not to the left.
Your action is an indication that your lower body is rotating too much late in the serve motion. If you kick your right leg back (as seen in both photos above), you might be able to drive up and forward more with your left foot landing in front of the baseline (and pointing in the direction of your serve when you land). The right leg kicking back will serve as a counterbalance and will also limit your lower body rotation after you have transferred your kinetic energy to your upper body, arm and racket.