Yes, but it's more than that. Excuse my rant below because I have a soft spot for this lol.
The "postmodernists" developed these ideas through a critique of capitalism, liberalism, colonialism, racism, sexism, etc. The rejection of grand narratives in theory was importantly an attack on these systems we oppose. Liberalism is the dominant grand narrative about the world which was/is used for uncountable crimes and continued existence, even as that narrative itself lost the plot long ago. This is why a lot of the "postmodern" authors were also readers of Marx. Marxists should question grand narratives about the world and people within it, even if that means we have to be critical of our own narratives.
The problem some communist orgs seem to have is a conflation of the "postmodernists" (by who they mean poststructuralists, etc.) and postmodernism as a defining logic within late capitalism. This is the same problem Peterson has. He literally doesn't even know what the words mean or who believes what, and neither do certain communist orgs. Like sure, be critical of the post structuralists, clearly their ideas were easily recuperated into the academy etc, but actually engage with it at least. I find orgs which use that term in such a hand waving way are just using it as a smoke screen to say they don't like gender studies and intersectionalism (both having their own relation to this trajectory in theory, and good criticism from a Marxist perspective), but generally not for good reasons. Which this org is clearly saying, but others less intentionally so.
The other important part is the relation to history. Postmodernism (read: global capital/spectacle/etc) treats history like its a grab bag of aesthetics to mishmash and sell again as a "new" commodity. In this sense everything loses its historical significance, its just aesthetics. It becomes a play, a simulation, kitsch, or a pastiche. But this also changes the way people inevitably see themselves within history, or whether they possess the capacity for effecting historical change at all. When everything appears to lose its historical character, the possibility for political change also seems impossible. In other terms, it's the superstructure reinforcing the base (global capitalism).
This peculiar relation to history is a problem for political organizing. Some left organizing may feel like it falls flat because of this postmodern grinder we find ourselves in. Where red aesthetics have already been eaten and spit back out by capital. Like it's hard for me to read the above excerpt and not just read it as an anachronistic larp. I've seen even good communist orgs put out some absolutely silly communiques written in a language that chatgpt could spit out if you asked it for "communist declarative article". (chat gpt is a good example of an invention which is deeply tied to both postmodernism in how it chews up language and without context spits it back out, and to the legacy of eugenics--the modernist triumph of statistics controlled by racists aka the ruling class.)
Jameson's book Postmodernism, Or The Cultural Logic of Late Capitalism is a great place to start. Just the first chapter is honestly enough.
A bunch of the text loooks very suspect and has several misspellings that point me in that direction.
Edit: I went and found the artist. I don't think it's AI slop, but it's so soulless it may as well be.
The primary media are easel graphics, mural art, digital art, and multimedia installation. Since February 24, 2022, Mykhailo has created military posters supporting Ukraine and volunteers. He believes in the power of visual signs because they can ignore geographical and language barriers, making their way straight to the human heart.
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Now is the time of stupidity