GFCI and 2 phase input
GFCI's don't care.

GFCI has no relationship with ground.  They don't care if the two wires are line-line or line-neutral.  In fact your GFCI's labeling reflects that.  

Also that is not 2-phase, it is single-phase with center ground.  

You didn't mention you are in the Philippines.  You don't have neutral, unless you are in the US-built territories that are still officially split-phase with a 3-wire feed from the transformer.  If you are only getting 2 wires off the pole, the thing in the middle is only your ground rod, and it is definitely not made for returning current.  If you try to hook a 120V load line-ground, in the Philippines, you will only electrify all your house's grounds.  

Also, using a step-down  autotransformer in the Philippines is a bad, bad idea.  Both 120V outputs will be hot, and it will be very important that you get grounding right.  In the Philippines you need an isolating transformer.