His father said it's a mug, the 'spout' is to fit the nose so that when one drinks, one can inhale the aroma at the same time.
They fill up the cup with Glühwein, not too full or the fire will be put out. A piece of sugar cube is placed on the spout end. The sugar cube is then drenched with high percentage alcohol like Schnapps and fire away ! The sugar will slowly caramalise and suppose to flow into the Glühwein. Then PROST !!