Capcom for the Nintendo Entertainment System, and based on the Disney cartoon of the same name. The game was a sequel to the 1990 game Chip 'n Dale: Rescue Rangers.
Re-released in 2017 as part of the Disney Afternoon Collection.
Unlike the prequel, this time the game has a real storyline that is told in cutscenes, although the plot is as creative as it is nonsensical.
Fat Cat escapes from prison (it was never mentioned what he was doing in there) and creates a diversion for the Rangers yet again during which he plans to steal the urn of the pharaoh (no other explanation is given) because it's full of evil spirits which he wants to release for unknown reasons. And it doesn't start to make sense from here.