The US does have more than 2 parties though. I think the argument being made is less about there being only 2 parties and more to do with how power is distributed. In a FPTP system, you will really only have 2 major parties that swap power around, even if a third party can attract a significant number of votes. That is essentially the main strength of FPTP, it almost always produces a dominant victor. In practice the Canadian system has seen power swap between the Conservatives and Liberals. In the UK power has swapped between the Conservatives and Labour. In India, power has swapped between the BJP and the INC. In Mexico there have only ever been 2 parties. I’ve tried to find more examples but unfortunately most countries with FPTP do not have good wikipedia pages for electoral results.
The US does seem to have a uniquely dysfunctional system, but I don’t really see any significant evidence from other countries with FPTP of third parties being able to enact real change.
Indirectly, pressure from UKIP led to the current Brexit situation—which as gjm points out, has not yet resulted in the UK leaving. However, UKIP’s vote increase didn’t cause Brexit, it simply led to a referendum. But the conservatives could have easily not called the referendum in the end since UKIP’s high vote share did not translate into any seats in government. I think it’s much easier to pin the blame on Cameron’s arrogance and putting party politics ahead of country, than it is on UKIP.
Nonetheless, even if you do not agree with that assessment, Brexit remains one data point. I am not personally aware of any other such events occuring in the likes of Canada or India, or similar examples in the UK.
I know little of the US pork barrel system, so can’t offer comment on that.