No. You cannot run PC games on a PlayStation 2. The architectures are fundamentally incompatible:
There is no PC emulator (DOSBox, Win9x, Wine) for PS2. The hardware gap is too vast. Even the PS2's own PS1 backward compatibility used the physical PS1 CPU (IOP) as a co-processor—not software emulation.
If you want to play PC classics on a TV, use a modern PC/HTPC, Steam Deck, or a Raspberry Pi 4/5 running x86 emulation (box86/box64) for very old titles—but not on PS2.