Currently fallen into a two party K-hole, sure.
But not intrinsically a two party political system and one founded initially by many who were vehemently oppossed to party politics.
A good question for the reader is how did the US political system end up in an unrepresentative quagmire of two parties to the effective exclusion of all others?
Is this the inevitable emergent outcome of that particular iterative rules based system?
Is some political variation of Hotelling's law at play here, can other voting systems help?
What happened in the last election, for example, is that "small C" conservative voters had no one to vote for. The actual Conservative party was unelectable, mired by scandals and gross incompetence. Labour party, the other one of the two, was anathema. Taking smaller steps to the left or right, you have the Liberal party or Reform, neither of which had any chances of getting a significant number of seats in the parlament.
In a healthy multi-party system, some other "small c" Conservative party would spring up to hoover up the votes. As it is, people had the choice of voting for a party widely seen as incompetent (including by its own sympathisers), a party that wants the opposite of everything they like, or a fringe party with no chance of shaping UK politics.
I have some theories as to why these happen at the same time... But anyway, it's not a uniquely American phenomenon.
People who are (say) Left-ish but not full blown supportes of BigLeftParty have the choice of voting for the major Left Party or an alternative left faction .. which is a wasted vote in a tight FPtP contest.
Worse a not BigLeftParty vote is one that effectively supports the major Right Party as it lowers the count for BigLeft.
Preference systems, Ranked Systems (there are variations) allow for direct first preference votes for a variationLeft Party with secondary fallback BigLeft preferences.
The direct support for not the main platform shows and causes deals to be made, the votes that fail to elect a variation still fall through and support the LeftWing while allowing the growth of alternative views.
Ranked voting fosters a healthy ecosystem of alternative smaller parties which can then grow, take seats, and help better represent the population at large with a diverse range of views, not just the BigTwo which end up as slightly variations of things not many support.
It's something everyone should look into. Some will get further than others.
A giant caveat is that mathematical impossibility in an idealised setting isn't quite the same as real world implementations.
A smaller scales the US first-past-the-post system worked tolerably well for some time.
Tweaked proportional does much better, pitfalls are rare and "real world" untidiness can address that well enough to reap the other benefits.
The subject of the video you linked is mainly Arrow's impossibility theorem which is covered early in a number of applied math | discrete math courses.
Plurality-rule methods like first-past-the-post and ranked-choice (instant-runoff) voting are highly sensitive to spoilers, [..]
By contrast, majority-rule (Condorcet) methods of ranked voting uniquely minimize the number of spoiled elections by restricting them to rare situations called cyclic ties.
Under some idealized models of voter behavior (e.g. Black's left-right spectrum), spoiler effects can disappear entirely for these methods.
The focus on no system being perfect distracts from bigger issues; which systems suck less than others, which systems result in better representation, which systems can doom spiral, etc.
An anecdote that I find has some[0] parallels:
In 1936[1], when the League of German Girls and Hitler Youth had open-air camps at the Nazi party meeting in Nürnberg, many came back pregnant.
This was enough of a scandal that they got rid of the girls' open-air camp in 1937; not only because one of new mothers named 13 people as possible fathers, but also because they were all going to be new mothers: Nazis had pushed to largely outlaw abortion in 1933.
see also https://en.wikipedia.org/wiki/Kinder,_Küche,_Kirche#Third_Re...
[0] albeit much sketchier than the 4/4 (elements of fascism), or 14/14 (Eco's elements of Ur-Fascism), evaluated in TFA.
[1] https://de.wikipedia.org/wiki/Reichsparteitag#:~:text=Zu%20d....
EDIT: another loose parallel: if you do a search for the word "Nazi" in german language newspapers, they occur pretty often in the years leading up to 1933, but after that year the word suddenly occurs only in foreign-published german-language papers — even back then, even the historical Nazis didn't like being described by that nickname:
https://www.deutsche-digitale-bibliothek.de/search/newspaper...
“Host Brooke Gladstone speaks with Jason Stanley, a professor of Philosophy at Yale University and who has written several books on fascism. He first warned about Trump’s fascist rhetoric in 2018, and explains why it's more important than ever to call it by its name.”
https://www.wnycstudios.org/podcasts/otm/articles/fascism-fe...
So we should have some solace that Trump has already been in office and unable to continue, did not lock Clinton up as he promised, etc.