I'm not sure about this odd little turret – it could be a reconstructed remnant of the mediaeval town walls or a fanciful folly.

The shoreline at the extreme left of the image, beneath the tree-covered slope, is the base of Gallows Point, a promontory (well, gravel spit) which accommodated one of the three most significant shipbuilding ports in Saxon Britain. This maritime heritage continued for centuries, with Beaumaris being the designated port of registration of all vessels operating from North West Wales.
As the name suggests, it was also the local place of execution.