Ok, thanks for confirming.

A string, as you described, would remain straight if it were in line with
the speaker axis, the direction of the soundwave. The speaker in the video
is projecting horizontally. But the water stream is vertical. If the string
were also vertical, it would also wave, much like a rope being shaken from
side to side at one end.

But there is probably a more important difference between the water stream
wave and a soundwave. A soundwave propogates; energy is continuously being
transformed back and forth between two different forms. Air motion causes
compression and rarefaction, compression and rarefaction causes air motion,
etc, etc.

The wave in the water stream is purely ballistic. Bits of water are being
sent out along varying paths in a repeating pattern. But there is no wave
propogation involved. You can see similar "waves" in traced machine gun fire.
Or if you just shake a garden hose rapidly.

The "wave shape" is there, even if directly observed. The strobe effect of the
video camera affects the wavelength and motion of the wave.

(edited - that should be "...affects the motion and direction of the wave".)
.