Not sure how to hook up new LED light fixture
Yes, what you're seeing there is the neutral terminal also being used as a splice.  Neutral comes from supply, and also goes onward to other unrelated equipment.  They are just making the splice at the lamp screw rather than up in the box at a wirenut, which is a little weird. 

I'd pull the two white wires off, clean them up and strip them (they might be one continuous wire looped over the screw, nothing wrong with that but it won't work with your new fixture) and join them with on a wire nut, yellow is the right color and Ideal brand is electricians' favorite. Your new lamp has pigtails so just add its white to these whites.