I can't tell you the purpose of the small building on the stone pier but have copied something from the internet about the place
"Pwllfanogl was once a busy little village on the outskirts of the large village of Llanfair PG with its own little shipbuilding industry. It was one of a number of little ports along the Menai Straits and served a commercial purpose.
During the 19th century you would have found a little pub here called ‘The Boat Inn’ and also a creamery and a working water mill, which is now a private abode and a storied level taller. A fabulous looking house as well.
Pwllfanogl played its role in Anglesey’s commerce, not only as a small port exporting and importing livestock and agricultural products. Intriguingly, there was a creamery that produced margarine in addition the mill that processed barley"