Grayson's movements dictate the actions of his on-screen Pokemon Red character. The Betta fish has been playing for more than 135 hours.
The project was created as part of a hackathon by two students,
Some viewers have expressed concern about Grayson's welfare on the messageboards of social site Reddit.
"Grayson's health and safety are our primary concern," wrote the creators of the feed, college students Catherine Moresco and Patrick Facheris in response.
They claim that the tank is heated and the water changed regularly - and they intend to get a bigger tank.
By 10:40 BST on Friday, 1,175, 673 people had viewed the real-time feed on Twitch, a website dedicated to live-streaming video gaming.
Pokemon Red/Blue was developed for the Nintendo Gameboy handheld console in the 1990s.
The aim of the game is to become champion of a fictional region known as Kanto by defeating eight Gym Leaders.
The developers said Grayson had already acquired his first Pokemon and defeated his first opponent.
The game was built in 24 hours during New York hackathon HackNY, according to its page on Twitch .
Another Twitch stream which invited multiple players to simultaneously control a single Pokemon character in one game ended in March.
The game was completed in 16 days and was watched by around 36 million people.