Postmodernism gets a bad rap because it can be abused by lazy people, but I think it possesses merit. Take
The Physical Impossibility of Death In The Mind of Someone Living. Yes, it's just a dead shark. But a dead shark can mean something. It invokes the fear of the shark, the fear of dead things, the fear of a living thing (like you) being stuck in a formaldehyde tank and paraded around years after your death for other living things to look at. It's not art with a plot, but it is art.
Or for something you're more likely to be familiar with, Metal Gear Solid 2, which was explicitly made to be a postmodernist video game and pattered off of the famous postmodernist book Simulacra and Simulation. It's all about the exploration of the idea that we don't experience the world as a real thing, but through the biological equivalent of batch searches called simulacra. It's why we generalize concepts more than we specialize them, and the reason people skew themselves out of the real world. Raiden (as the player) conceives of war through VR simulation and so treats it as being like a game (with the irony that MGS2 is in fact a game). He's weird and kind of deluded, because his conception of violence was framed a certain way and is reluctant to move from that way. Then, in the last third, Raiden stops being a meatpuppet of the player and starts to act under his own identity, showing that he is in fact already
very mired in the absolute horror of killing through being a child solider in the Liberian Civil War. This culminates with the ending, where still kind of mindfucked by everything that happens, he fully rejects his role as the main character by throwing away the dog tags you made at the start of the game and just walks off into New York. It's also somewhat positive towards the idea of meaning for a postmodernist work, what with Snake talking about how any memetic influence you leave behind gives your life purpose, and that you should embrace that.
There's plenty of other angles in MGS2, like the GW being the representation of the simulacra that is American political culture, but I'll let it drop there. And no, it doesn't mean it was all a computer simulation, that's not the kind of simulation it means.
I'm also going to take a moment to defend Dadism, which is not explicitly postmodernist only because it predated it. This is the "fuck you, that's why" justification, starting with Henry DuChamp's The Fountain. What people don't get is the message is not "anything can be art", the message of the "lazy art" is "fuck you". It's a tongue in cheek protest, not meaninglessness. The Fountain was "made" in response to DuChamp's disgust with his art colleagues playing ball with the nepotistic and corrupt New York art scene at the time. The message was "you think we should only have art from our friends? Fine, here's your 'art'. Also, you all drink piss, fuck you." It requires a certain level of context to not look stupid.
Incidentally, a lot of modern non-sequitur internet humor is also dadist in nature.