http://www.youtube.com/watch?v=R4--IqUDugs
Fish definition- Radically short stubby board(under 6ft), fairly thick developed from kneeboards in the 1970's by Steve Lis. Primarily Twin Fin set up with a swallow tail shape and popular in smaller waves. Note, any type of board (such as shortboard or mini-longboard) can have a fish tail, and these are commonly referred to as a "fish", but they lack the other properties of a fish as listed here.
That is the retro fish. Modern developments include the quad fin set-up added to the retro design and more modern rails and bottom contours with stepped in tails. These boards still retain the flat rockers and wide short outlines.
The modern fish as it gets called, is usually a shortboard with a swallow tail and or a quad fin set-up.
In my opinion to qualify as a modern fish (but with a shortboard outline, ie the board needs to be wider than your average shortboard and to have less rocker than your average shortboard, quad or thruster set-up. Doesn't need to be thick either.
Just my take on it.
So the board you've listed in my opinion could be a modern fish, but that depends on the rocker and the width of the board.
But bewilderbeast is right that board would struggle as a twin.
KS