Client for PlayStation 4 and PlayStation 5 Remote Play for Linux, FreeBSD, OpenBSD, NetBSD, Android, macOS, Windows, Nintendo Switch
So no
Even if it was possible (which it probably wouldn’t be with a Pi Zero 2 inside and a software porting project that it’s unlikely anyone would even attempt), the display on the PicoCalc wouldn’t refresh fast enough to make anything playable anyway, and the keyboard would be poor set of gaming controls. You could probably do it with a uConsole and a CM4 or CM5, but even that wouldn’t exactly be ideal for gaming.
You’d be better off getting a Steam Deck. It apparently can work well on that, and it’s a device actually designed for playing games. 
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