As I pointed out, we can look at the tangible outcomes in China such as poverty reduction programs that simply aren't happening in countries where capitalists are in charge. So, we don't have to take their word for it, we can just look at the outcomes.

It's also worth noting that 87.6% of young Chinese identify with Marxism, and the party has 95 million members. People in China learn about communism in school, and I think it's reasonable to assume that a country where vast majority of young people identify as Marxist, would have a genuine communist government in charge.

Another indicator we can look at is that China doesn't suffer from regular crashes seen under capitalism. An inherent contradiction within capitalism is that the capitalists always want to cut pay for their employees to minimize the costs, while they also require consumers with enough spending power to consume the commodities they produce. This is why capitalism results in regular economic crashes when wages fall below the point where consumption can keep up with the rate of commodity production. At that point you end up with overproduction and a crash. If China was capitalist then it should be experiencing these kinds of crashes regularly just like actual capitalist nations are in the Western world.

Working conditions and wages in China are improving rapidly. Real wage (i.e. the wage adjusted for the prices you pay) has gone up 4x in the past 25 years, more than any other country. This is staggering considering it's the most populous country on the planet. Social mobility in China is actually higher than it is in US.

Another example of the difference in China is that it massively invests in infrastructure. They used more concrete in 3 years than US in all of 20th century, they built 27,000km of high speed rail in a decade. This is another thing we don't see happening under capitalism because capitalists don't see significant profit from infrastructure investments. This is the main reason US infrastructure is currently crumbling.

Finally, 90% of families in the country own their home giving China one of the highest home ownership rates in the world. What’s more is that 80% of these homes are owned outright, without mortgages or any other leans. This sort of home ownership is not seen in capitalist countries where housing has become a commodity.

The reason capitalists run the countries even under Nodric model is because they are able to use their wealth to create disproportionate influence on the society. Capitalists own the media, provide funding for political campaigns, and so on. This allows capitalists to run a propaganda campaign against the population of the country. A couple of excellent books on the subject are Inventing Reality and Manufacturing Consent.

And in fact, we do see this system erode over time. Here's a discussion of what happened in Sweden since the 70s and how capitalists have been eroding social programs there https://jacobin.com/2019/08/sweden-1970s-democratic-socialism-olof-palme-lo