How does an external tower style bathtub drain work?
It's called a "standing waste".  It works just like you say.  The cone at the base of the inner tube seals against a flange and the water must fill the outer tube (attached to your floor) before (over)flowing down the inner tube.  Here's a pic since words are useless for describing this kind of thing.



Here's some in-depth discussion on resolving a clog on one of these.

if you see water in the tube at the same height as in the tub, you should snake down the tube.  If not, the blockage is between the drain and the standing waste and you should snake down the tub drain.

I suspect the blockage is downstream of the standing waste since the plunger was ineffective.  Try sealing the top of the standing waste tube while plunging before resorting to the snake.