While we know sound is a longitudinal wave, then in the linked video why some sort of transverse nature is felt? In this video, why does the longitudinal nature along with transverse nature is felt for sound wave?
Is this because of the tube(containing the vibrating particles)?
 A: Sound waves in gasses (air), and in liquids, are longitudinal.  What the video shows, is a gravity wave in the surface of a liquid, driven by
coupling to a sound wave in air.
Gravity waves only have vertical polarization (they rely on
the gravity force for propogation, and propogate perpendicular
to gravity).   It is possible that the tube is part of the
coupling, but more likely the in-air standing wave directly drives the
liquid surface.
A: I believe that in the video the "particles" (or whatever those small ball thingies are) are just laying on each other due to the pressure of the wave-field in the tube (a standing wave that is). There are some planes with high pressure which in turn push the small particles towards the nodal points of the standing wave. This concentration of the particles just makes them move on top of each other to occupy the space where the pressure is minimal.
Of course, their mass and the forces acting between them counterbalance the forces acting on them due to the pressure increase and this is why they don't occupy only the nodal planes. In addition to that, you have to keep in that due to the lossy nature of real systems (such as this tube) you won't see any ideal standing waves, but you'll see that there's some non-idealities there (non-constant patterns, etc.).
