Looks like he's on a conference call and holding the phone so she can see the inauguration.
I don't think he was following the camera. The camera would be a long ways off and using a zoom. Probably from up on that tower in front of the capitol. It looks like he just adjusted it in his hands, it can get a bit tiresome holding a phone up like that for an extended period.
I don't see a mask or "tape". It is a very long-distant shot with a zoom of a small phone screen glared in the direct sun light and not at a direct face-on angle, with a news camera broadcast to YT. Pixels are abundant and a clear image is near impossible.