What I think would be more interesting would be a way for viewers to stimulate the fish.
Say you have a link that charges the viewer a small fee to feed the fish on a certain side of the tank. Scale the price with how much food the fish has been given (all the way down to $0.00 and up exponentially to not overfeed the fish). Basically, let the internet handle feeding your fish.
I don't think this is a possibility. While you could get some sort of feedback loop going (fish gets hit it gets shocked, fish hits it gets food or something), there would be no way for the fish to understand the massive amount of information they'd need to grok from the game, so they'd just be getting all this random stimuli with nothing to attach it to.
I can't see anyway to bridge the gap of making the fish understand the stimuli in relation to what's going on in the game. I would imagine the same is true for rats.
The fish doesn't need to grok the entire game, it just has to be better than the other fish. (Cue that joke about two people being chased by a bear and one pausing to put on his sneakers. "What are you doing? You can't outrun a bear!" "I don't have to, I just have to outrun you!")
For example, if fish A realizes that swimming around corner X gets it food, because X happens to correspond to "move forward and punch", that's enough to win the game if fish B doesn't figure out the same.