Figured it out for myself, but I'll post the answer here in case
anybody else ever searches for this:

The teflon seal seems to work well below the spray arm, and not around
the shaft of the spray arm. I removed the spray arm, removed the
gear-shaped nut and old gasket, put the new gasket on and then
carefully tightened the gear-shaped nut to ensure that the gasket was
in place, then replaced the spray arm.

When the dishwasher is off, the spray arm rests on the gasket. It
turns (relatively) freely, though it would probably wear through
quickly if it were like this all the time. Although I can't see in the
dishwasher when it's running, I would guess that the water pressure
levitates the arm above the gasket and prevents too much contact.

The dishwasher cleans much better now.

This was a Hotpoint / GE HDA465-01.

Mike