A synthesizer player would never have guessed this to be a Theremin for a couple of reasons:
The portamento is identifiable as a "linear" response. A linear portamento moves at a set rate to the target note and stops abruptly on the target note. (An exponential portamento moves faster on large intervals and slows down as it approaches the target note.)
To glide for 4 or five octaves at a steady rate is virtually impossible on a Theremin because of the non-linearities... even on the most linear Theremin. Also, just stopping on the target note after some of the rapid glides just wouldn't be possible.
Moog synthesizers have a "linear" portamento response. Also, judging from the large sweep at the beginning, the keyboard would be a large (61-note) keyboard which suggests a modular synth (which would have been available in 1969).
Another tip-off that the sound is NOT a Theremin is that the tape echo is really only noticeable on the sweep -- when holding a note the echo "disappears". Highly unlikely that a Thereminist would hold a note so still that one would not discern an echo.
There is no shading on the volume which suggests a non-touch sensitive keyboard -- certainly not a Theremin.
Given the precision of notes I wouldn't suspect a Synthi or Buchla type keyboard (touchpads instead of keys). The notes are too precise and rapid for a ribbon controller or a tannerin.
So, my guess is a Moog Modular.