The “square ring” silicone part fits around the stem like a rubber band and settles-into that notch, so that those little wings on either side effectively form the top bits of the stem rails.
The bottom dampening comes from a little silicone disc inside the bottom of the tube that the stem pole bottoms-out on.
As far as I know, all TTC silents work this way - and their half-silent switches have normal stems paired with those plugs in the housings.