First, there is a bit of a “cooldown” on swing hits. You can only do a swing once every 0.2 seconds. So when you are wiggling your sword through the dummy back and forth really quick, it makes sense that it only does the first hit.
Secondly, those slash effects are basically the server telling you that the hit happened. When you hit an enemy, your controller should vibrate instantly and then tell server that you hit something. Once server hears of your hit, it sends a signal back to you to show a visual slash effect and the damage numbers. So if you want to get a feel for what your ping is, do a sword hit and see how long it takes for the slash to show.
Things look to be working fine. Near the end of the video, you slowed it down a bit and was hitting your combos.