Interestingly, despite the mention of the theoretical perfect score (1,265,000), I've never actually seen the calculation for that. I've also never seen a TAS of Donkey Kong aiming for score; if that perfect score is actually achievable, it should be possible to construct a TAS that does so.
"a random number generator determines the value of many of the prizes you encounter and the path some of the obstacles take."
Seemingly, you would still need several TAS-tries because of the RNG, right? (Unless you can rewind and the 'random' is calculated as a function of something separate from the running instance of the game.)
Some games have mechanisms to manipulate their RNG and it is even used in some TASes.
During this year's SGDQ's TAS block they had a TAS of a Sonic game that used exactly this technique: the bot waited at the title screen the exact amount of frames to manipulate the seed of the game's RNG.
Botting the whole game for perfection involves a huge number of permutations since it's a dynamic system. But fastest time is arguably a less complex problem than maximum score since fewer of the RNG events "matter" to time attacks. In a game like Donkey Kong, maximizing one score-relevant event may take away from another.
My favorite RNG manipulation is the King's Bounty TAS:
If you don't get it, here is the summary: To win King's Bounty your hero must find and dig up the randomly-located Sceptre of Order. This normally means questing around for map pieces, combat, recruitment, etc. But with some RNG manipulation it can be placed right outside your starting point.
The run posted actually improved upon the previous one with a new bot that does a more exhaustive search.
Yea, I saw some of the runs during Summer Games Done Quickly that involved some attempts at RNG manipulation although it was not obvious what was happening at all to me watching at home.
It's a very good documentary, but I've heard that it's edited in such a way to make the original highscore holder look like more of a villain. Not to mention that the highscore changed hands several times over the years, but it was presented as though it had been held by one guy for the last 20-30 years.
A moderately inquisitive person would think from the title of the article that this would be related in some way to the movie.
One could then ctrl-F just in case, to see if it's referenced, and still get away with pretending to be interested in this stuff without spending your time actually reading.
I can only assume you've also not watched the "amazing" documentary you've cited.