This is a tannerin, not a real theremin. It is played with a slide (similar to a ribbon sensor), and the most known performance with this synth is Good Vibrations by the Beach Boys (Pet Sound album, 1966). Brian Wilson plays the instrument adviced by Paul Tanner, who was at the time using the instrument, build by Tom Polk.
The Tannerin is an electronic instrument that produces a pure sine wave, variable over three or four octaves. It is played by sliding a knob along the length of the instrument, on some models starting and stopping the tone with a contact switch located on the pitch knob and operated by one’s forefinger. You can see the video how Brian Wilson plays the tannerin: