Yep, I've seen this before. It may have even been posted on here several years back. I'm surprised that a video recording from 1965 is in color.
This instrument does a lot more than what the Mellotron eventually became. As far as I know, the ones you usually hear on rock records are basic, one-keyboard instruments that allow you to select between two tones that are, of course, played on tapes inside the instrument. If you want different sounds, you have to change the whole set of tapes. But it was a way to get the sound of real instruments before electronic sampling technology was available.
The instrument in the video is far more complex, with all of those rhythms and backgrounds, and it sounded like he said there is a choice of 18 instrument sounds for lead instruments! That thing must have been jammed full of tape loops/strips!
But I imagine the accompaniment section had to be pretty limited, as it would seem difficult to accommodate a wide selection of drum rhythms, chords, tempos, and background instruments using just tape loops. You could change the speed of the playback, but that would affect pitch and tempo at the same time.
Mellotron does still exist, and I think they do sell a tape-based system. But they also sell electronic-based systems, as well. But in my opinion, they're very expensive for what is essentially a "rompler" -- as much as $2800 US -- with keyboards like the PSR-SX700 and SX900 having far more features for the money.
On a related note, what do you think was the first commercially available polyphonic synthesizer? A Moog from the 1960's, maybe? Nope! It's the Hammond Novachord from 1939! Just do a search for it -- plenty of info out there about it. Wikipedia says it had 163 vacuum tubes, and a few still exist today!