A shut door is a key plot point in Lauren Yee’s “King of the Yees,” but the Signature Theatre production draws us right into the play’s profound yet funny world. The visions we encounter there — a fairy-tale quest involving whiskey, a kung fu-evoking news bulletin, an FBI operation that unfurls like a slow-motion John Woo thriller — are so delightfully quirky that you hardly want to cross back across the threshold.