Phone switches to watch interface when put against a specific side of my laptop
The tiny watch screen is a feature of LG G2 named QuickWindow when put on a smart cover (a cover that uses magnets to detect if it's closed or opened).



(LG G2 showing tiny watch when put on smart cover)

That indicates there's a magnet field on a particular spot on ASUS Zenbook, and LG G2 reacts to that on a very specific position. (As already confirmed by OP, there's a magnet on the left side of the lid to keep the laptop closed)