The handfish has a very similar type of locomotion: https://en.wikipedia.org/wiki/Handfish , also: https://en.wikipedia.org/wiki/Ogcocephalus.

And the tripodfish stands on a tripod :) : https://youtu.be/yOKdog8zbXw

And on land, there are mudskippers, which are amphibious and have efficient terrestrial locomotion.

See also the walking sharks: https://en.wikipedia.org/wiki/Hemiscyllium_halmahera

Various species of bottom-dwelling or feeding fish have independently evolved pectoral fin modifications to assist their locomotion across the sea floor.

I wonder how "Found in a beach, spotted in shallow water, and nobody knows where the fish came" ended being translated to "is a deep sea fish".

Nope. Most probably a reef fish living around -20m or so. Is an interesting species in any case.

UPDATED: Dorsal and anal fins discard Allenichthys. Body rough so is not Phyllophryne, no ocelli in body or tail fin, conspicuous esca (so is not Antennatus), first and two dorsal elongated (so is not Histiophryne):

It seems from genus Antennarius.

They probably didn't mean "deep sea fish" to be taken littorally.

Have anyone been able to find more photos? Only found this one: http://www.nzherald.co.nz/lifestyle/news/article.cfm?c_id=6&...

Yes, there is a third photo of the opened big mouth in Facebook, but do not adds much new info. The ilicium shape and lenght is not clear and there is not info about the size of the fish.