There is also the time travel paradox that if someone did time travel (I personally don't think they did) and was seen on video, they could simply go back in time again and get themselves out of the video thus it would have never happened and YouTube would happily go on showing stupid cat tricks today.
IF (and that is a bing IF) this is some sort of communication device then I would assume it was an alien in disguise. The fellow does point out that it is a very 'butch' woman. I think a little grey could easily sneak under that heavy coat.
Personally I think it is something mundane that is common in the era. The guy who walks past her doesn't bat an eye. I still give a double take to people on Bluetooth headset when I don't see it so I am sure a lady talking into an ear box would turn some heads.