The whining sound is likely power steering pump. Loss of fluid usually comes from the hoses that go to the pump. Factory uses insufficient crimp on clamps. Install some hose clamps on the lines, fill reservoir to appropriate level on dip stick. Then leave the cap off, start car and turn wheels from left to right (do NOT let steering wheel lock) for a few minutes. If noise get's worse check fluid and add as necessary then, repeat the process until noise is gone.
There is a distinct squeeling I can hear in the video that sounds like a pulley bearing but, could possibly be the power steering pump or belt tensioner pulley.
Note: The power steering pump is a PITA to fill. Will likely require a funnel with a hose attached. You must poor in a little, pull the hose out, put cap on and tighten, pull cap off, and check level. GM royally screwed up on this design.
So, I finally got around to changing the belt tensioner pulley today (cheap and quick) but after driving around some, it's still making the same noise. Could it just be another pulley that needs to be changed?