The TIA was designed by Jay Miner while he was working at Atari. I'd be very surprised if Atari did not hold whatever rights could be held.
That being said, the rights that could be held to an IC design at the time were much more limited than they are today. Before the Washington treaty of 1989 and TRIPS, ICs were protected only by patents, not by copyright, ...
There is a New York Times article (The Game Turns Serious at Atari from December, 1982. One quote from it is:
Atari is also facing problems in its two other businesses. Its arcade game business has dropped into the red this quarter and its home computer business, which has never yet been profitable, faces a market-share battle.
(the first business is the ...
So: what's the core idea of this algorithm?
It looks like some variation of a linear-feedback shift register. These look at some of the bits in the value, and then produce another bit which is shifted in to form the next value. They can be made to loop through (almost) all possible values of a word, and so have even been used as program counters.
I think it would be unlikely to work on computers, as opposed to consoles.
The trick relies on corrupting values in RAM (by disrupting the DRAM refresh cycle) without also corrupting the game code; this worked in the arcade and on consoles, where the game code was held in ROM and could not be corrupted.
But on a home computer, games were normally loaded ...
(This is years after you solved it but just for completion...)
An inelegant method that doesn't involve taking a pot' apart is to spray switch cleaner (e.g. Servisol) into the pot's insides then turn the pot's knob back and forward to the limits a lot, say 10 times.
Do that a few times and they're much better, often good as new.