I took a look at the video. I see your doing something very different than what i'm doing. It looks like you've got things running properly. I assume your using the mouse position and moving the entity directly there? By the looks of things, I dont think you'd ever need to constantly update your players position(if it keeps moving to where mouse clicked). The only position you should send is the mouse position(upon clicking) and send it reliable.

All along I thought you were doing something realtime(user input via keyboard), lol, but I guess multiplayer coding techniques can be very generalized and work across all genres.