I apologize for the delay in getting a response on this, but the team has been busy working on patch 1.19. We showed the video to Yoshida so that he could respond to what is being demonstrated in it. Please find his response below:

Quote Originally Posted by Naoki_Yoshida
The issue where character movement routes are different on individual clients [such as that demonstrated in the YouTube link from the original poster] is not actually due to server lag, but due to a conflict between animation control and a process that supplements movement routes by using character coordinates and vector/speed.

Even with the current status, the server is working and judging coordinates and routes properly at the point of synchronization. (Coordinates are being processed with an intended frequency so that the difference in coordinates themselves is almost none.)

Therefore, corrections to the animation and the process to compensate movement routes will improve the cases like in the video. Improvements to the server-related issues will be another story. Although the previously mentioned correction will not be made in patch 1.19, it will be done after the patch.
As you can see, there are many systems in play when it comes to the server/client relationship, so the overall term 'server-related adjustments' actually encompasses quite a few different things. This is just another step we are taking to improve the overall situation as development continues to address issues moving forward.