If a government meets every point in the definition of fascism, it's fascism, regardless of what it brands itself as.

From the essay you were linked:

China, on the other hand, still matches up with the original unadulterated definition of fascism since it’s far-right i.e. extreme nationalist, nativist and authoritarian. It has an unabashed dictator i.e. the Paramount Leader of China, who simultaneously holds the positions of head of state, government, civil and military offices of the highest order within the party...

It has a forcible suppression of opposition in the form of re-education camps, outlawing of protest, institutional rape, mass-censorship, an intricate government propaganda system and staggering numbers of political prisoners. It has strong regimentation of both society and economy: The state has long acted to purge anything that doesn’t meet with strict hetero-normative Han-nationalist ideals, even outlawing LGBT representation in the media, and maintains an iron grip on the economy to the point of putting government officials to work full time inside at least a hundred big corporations.

Fascism is also always corporatist in nature, which the CPC certainly embodies with its forced class collaboration between worker and employer, and the way it structures its whole economy around the growth of the corporations, which serve to grow the state and its imperialist expansionism.

The party’s corporatism has all the usual features including useless employer-controlled unions and a staggering 1.5 million-member police force which springs into action during any class conflict, using its monopoly on violence to uphold the interests of the bourgeois class and violently put down the workers.

China is implicitly a fascist nation in the most traditional sense, meeting every word of the original definition, with the power in the hands of the head of state seemingly for as long as he wants it.