Well, I tried thinking about the effect, and how it could be obtained WITHOUT need of any exotic materials. I have no knowledge whatsoever of how the fellow is actually doing his trick, but here's one way to approach his results: make the front and back glass (or plastic) faces of the tank so they can slide vertically. When he "shoots" the cards at the front, the front face moves upward to reveal the card glued inside by a confederate hidden in the base below the aquarium itself. "Ordinary" stage-magician's methods should more than suffice to palm the card and pass it to that person, who attaches it while the magician shuffles cards and otherwise works the crowd. Around back, the second movable face has a conical "porthole" with a clear plastic adhesive hinge, probably at the top. The magician pushes it inward to introduce his arm after the opening is raised into position by that same confederate. The paper towel, or whatever it is, hides the circular outline from the crowd during the rise. The end view has seaweed and other distractions so that such a hinged plate could not be seen. After retrieving the card, the magician permits the door to close, and it is withdrawn downward along with the entire face, leaving an unmarked surface.
As I said, I do NOT know how this guy does it, but that's a plausible way to make workable props to obtain the same effect.
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" Ignorance and arrogance have more in common than their last four letters. "