The chess engines used in both games were licensed from the same developers; Mattel didn't have the expertise in-house to implement a chess game entirely from scratch. Here is a snippet from the Aquarius Chess trivia file in the Aquaricart:
"Like the Intellivision's USCF Chess, Aquarius Chess features a computer opponent which was not programmed at Mattel, but was implemented using a chess engine licensed from an outside company.
Heuristic Software Corporation was founded by chess player Julio Kaplan, International Master and winner of the 1967 World Junior Chess Championship. At his previous company, Teletape Productions, Kaplan recruited programmer (and fellow chess expert) Craig Barnes in 1980, and together they developed the chess engines which were used in Mattel's Computer Chess handheld and in USCF Chess for the Intellivision. After completing these projects for Mattel, Kaplan left Teletape Productions to start Heuristic Software in 1982, and Barnes joined him as Senior Programmer.
Heuristic Software developed the chess engine for Aquarius Chess, along with many other intelligent strategy games and other consumer products (checkers, chess, bridge, calculators, combination games, etc.), before closing its doors in 1995."
(The user interface for both games was designed and programmed at Mattel, on the Intellivision by Russ Ludwick and on the Aquarius by Stan Summay.)