The gait is a genuine walk. The epaulette shark moves its pectoral and pelvic fins in an alternating pattern comparable to a salamander's, allowing it to cross reef surfaces where the water is only centimetres deep, and it can persist out of water for short periods.
The physiology behind this is more striking than the walking. In laboratory studies epaulette sharks survived hours of severe hypoxia and complete anoxia at reef temperatures by reducing brain and heart activity, lowering blood pressure, and selectively shutting down neural function without suffering the tissue damage that would follow in most vertebrates.
That resilience has made the species a model for research into oxygen deprivation and reperfusion injury. It has also fed an overstatement: the species is not immune to warming reefs. Experimental work shows that higher incubation temperatures accelerate development and produce weaker, less efficient hatchlings, so the walking shark's tolerance has limits.