Please note the Atari 2600 Chess game was all on a single 4096 bytes (4KB, not 4MB or 4GB) ROM chip. It did not have lots of game strategies, it did not have a vast library of games stored to draw on. It had 151 total machine instructions versus I believe between has over 1000. The clock speed was 1.17MHz versus 3+GHz. The instructions took between 2 and 7 clock cycles each (depending on instruction). The modern chips have more REGISTER space than the that chip had total space.
The game had no ability to store chess games and strategies. The 4096 bytes was for BOTH instructions and data.
Suggesting the AI could have won with Deep Research mode, which based on that name I assume it would be going out and accessing literally dozens if not hundreds of books on famous chess matches with move by move analysis is probably correct. But consider the AI in even its most basic mode was probably provided with more information on chess strategy that the Atari could ever begin to hold.
The chess software as small as it was, probably less than 2000 bytes for instruction area was indeed dedicated to playing chess. That 2000 bytes had to hold all the possible moves for each piece which probably took about 16 bytes if stored in bit mode, then the rest was calculating moves and comparing results maybe up to 4 moves in advance (remember limited storage for holding current positions and then working out future positions).
This is an example of throwing tons of tech and dollars at trying to solve a problem (beating the Atari) using bad code.
Artificial Intelligence is NOT intelligent. It is just a massive data collection program that then looks for possible relationships and reports them. A computer will never understand what an apple is, what left is, what sky is, or what any abstract idea is. It is just a machine which processes what it is given. Does AI sometimes find relationships never noticed by humans before, yes. Does AI sometimes notice research avenues never attempted by humans before, yes. Does AI sometimes find relationships in bits and pieces of research from many different papers working on, to humans, unrelated things, yes. But it is not intelligent, it is able to simply review exobytes amounts of data for possible correlations, relationships, and cause and effect.
No, if I understand Deep Research mode (again based on name), the AI would still not beat the Atari 2600, it would simply find answers in books, essentially plagiarizing old games.