Sorry for the barrage of questions, but there's not a lot of info to go on here.

So homing works fine, and printing works fine. Just manually commanded moves and the X0 Y0 Z250 in your ending gcode don't work. Correct?

The video quality isn't all that great, but I see all three axes moving in each of the movement bursts. Is that correct? Exactly what is going on with the printer during the video? Are you homing, are you jogging, or running gcode, or...? Are you doing something (another command, another button press, etc.) to cause the printer to start another movement burst?

Are you running the firmware that came preinstalled on the board, or have you upgraded to something else? If something else, what, and how did you go about the process of setting the firmware configuration parameters?

Am I correct in assuming the X0 Y0 Z250 you talk about is part of single line added to your gcode end code? Show all of your ending gcode. How are you setting the speed parameter? Note that all on one line will also force a 3-dimensional move that might take forever. Move x&y a little bit... Now move z a little bit... now x&y again... etc. Try simplifying the move planning by putting the X0 Y0 on one line and the Z250 on separate lines. I usually raise Z up before I move x&y to ensure the nozzle doesn't drag across the print.

How are you commanding the jog? From the LCD panel or from host software? If from the LCD, what step size (10mm, 1mm, 0.1mm)? If 0.1mm, do you see the same problem with Z if you try 10mm? If from host software, what host software (Pronterface, Repetier Host, etc.)? Also if from host software, how have you went about configuring it for maximum movement speeds, etc.?