It does sound like the belt is flapping around, but I'd be wondering why, as unless somebody has recently been slackening the motor of, it shouldn't suddenly become slack. However the spindle does seem a bit noisy in general, but that could just be the video.

Also it heating up that quick is not a good sign. I'd be taking the motor of, and giving the spindle a spin by hand to see how it feels. I'd also be checking for play with a DTI, but to check for correct adjustment, you really have to take the cylinder and the top support housing/bearing of, as the top bearing will mask any play in the main spindle bearings.