Specific trumps general. In this case it says that you're using "part of your movement" which really onyl happens during a move action (generally). Presumably you could also do it during a charge (though I dunno how it affects charges) or a run action (same caveat). Even a 5 ft step, though in that case you would only be teleporting to an adjacent square, so not very helpful.
Mostly this power just seems to allow you to bypass terrain restrictions or other spacial effects; you still have to use movement squares equivalent to how far you move. I'm sure someone will speak up if I'm mistaken on that, so it won't hurt to listen for a few days to get the correct answer. ;)
