The back story, as according to Blabbermouth.net:
Bassist Bob Daisley, who was a member of Rainbow from 1977 to 1979, has posted high-quality video footage of the band performing the songs "Gates of Babylon," "Long Live Rock 'N' Roll" and "L.A. Connection" at a New York studio prior to the release of the band's third studio album, 1978's "Long Live Rock 'N' Roll."
Although Bob Daisley and David Stone are listed on the "Long Live Rock 'N' Roll" credits for their contributions, they joined Rainbow after the recording sessions had already commenced and only appear on a couple of tracks. Guitarist Ritchie Blackmore played most of the bass parts himself for the album.
They are pretty obviously miming along but the vocals are for sure different from the record so maybe those were live. Regardless, these are pretty cool. Enjoy:
Gates of Babylon
Long Live Rock N Roll