The footage was made specially for 2001.
According to Creating Special Effects for "2001: A Space Odyssey" by Douglas Trumbull
The movie being shown on the TV set in front of the sleeping passenger was a little more complicated. Kubrick wanted shots of a futuristic car, and close-ups of a love scene taking place inside. A crew was dispatched to Detroit to shoot a sleek car of the future which was provided by, I believe, the Ford Motor Company. The exteriors were shot in 35mm, but the interiors were shot without seats or passengers, as four-by-five Ektachrome transparencies. Using these as background plates for a normal rear-projection set-up, on actor and actress were seated in dummy seats and Kubrick directed the love scene. Shot on 35mm, this was cut together with the previous exterior shots, and projected onto the TV screen using a first-surface mirror.
There's a colour photo of the actors and the car at http://www.iamag.co/features/2001-a-space-odyssey-100-behind-the-scenes-photos/

and some speculation about the actors at http://www.2001italia.it/2013/08/whos-that-girl-actress-spotting-in-2001.html
(Thanks to Rob Manuel for the tip-off)