So they're not using a "standard" oscilloscope, as it would be impossible since it needs at least 2 different signals (X and Y ; otherwise you would just get a diagonal line). They're using an oscilloscope which has a special mode that causes it to render the video signal differently.
The "dual screen" feature is a simple trick, and almost cheating () : the two screens are calibrated differently, so each of them show a different part of the picture. In theory you could do the same thing with standard TVs or video monitors, but you would need to make the image twice wide (or as high), and normal screens don't allow such extreme ratios, unlike oscilloscopes.
It's still impressive of course
I was thinking about other ways of doing this kind of stuff.
First, the TV image is B&W so it would suggest that a low-pass filter could be used at the TV input to keep only the luminance part, leaving room to higher frequencies for the oscilloscope.
Then use something along the lines of a sync separator circuit to achieve a X/Y display for the scope.
Time-wise, it may be possible to use the blanking period too.
Well, looks more like Star Trek electronics than anything else, but maybe someday it would be worth a trry