Does it require scripting?

I used GetActorZ ACS function, but from a script, triggered by crossed line. I think it's possible to run an endless script, which repeats over and over again, but there's a problem - which actor to check. Player can't be tagged, and without tags GetActorZ works only for actor who triggered something (pressed switch/crossed line). Um... so I actually think it's either not possible or requires some tricks. OTOH it is possible to create new "detecting" class in progs. There are already such classes for "player hit floor/ceiling" etc, we can use them as an example. Or rather my own Funnel class which I wrote for KA, it made checks of player's Z position in the certain sector.

How does the original Hexen teleport work in the 4th hub (the place where you fall down a deep hole from a cave and then get teleported to another map)?

You cross over the cliff linedef, then there's a delay before it changes.

Yeah, AFAIK it's simply timed.