Perhaps it might not to others, but for noobish people like me it seems incredulous that horseshoe crabs actually swim upsidedown! And some of us were lucky enough to witness it during one of the coral spawning. Most of us thought that it was probably an injured or dead horseshoe crab floating face up on the water surface. Mr Lee scooped it up and the crab turned up to be a perfectly healthy one, because it was struggling so feriously on the boat.
Horseshoe Crabs are actually not crabs but more towards spiders. They are also commonly known as "living fossils" because they have changed little for hundreds of millions years. The Coastal Horseshoe Crab, Tachypleus gigas, is one of the two species of horseshoe crabs found locally, identifiable by its triangular and serrated tail.
Did some online surfing regarding this peculiar sighting. Apparently, it was just because of a mere physics and hydrodynamic thing. From Vosatka. Ohio Journal of Science. 70 (1970): 276–283, it was stated that this inverted swimming was due to its body design with the sloping cephalothroax helping to lift itself upwards when it swims. If it swims rightside up, the animal will just keep sinking. The legs of the horseshoe crab as well as the book gills provide propelling force while its tail serves as to nagivate (beside flipping itself up when overturned).
Above shows the swimming process of a horseshoe crab extracted from the journal. Below is a youtube video of a baby horseshoe attempting in vain (from 20s onwards) to swim.