what type of fighting fish

I'd say it was good old Betta splendens. Standard species. Someone has just done some selective breeding so that the membrane between the fin rays is concave, giving the spiky look.

I have to say I prefer the standard. More graceful IMO.
 
I didn't say it was the standard variety, but that B. splendens is the standard species of fighting fish.
 
AquariaCentral.com