Yes. Metal Gear Solid (1998) is a PlayStation 1 game. The PS2 is natively backward compatible with almost all PS1 titles—just insert the disc and play.
Use a PS1 memory card to save (PS2 cards don't work for PS1 games).
Graphics: enable "Texture Smoothing" in PS2 system settings for slight upscaling.
Disc read issues? Clean the disc; early PS2 lasers struggle with some black-backed PS1 CDs.
No emulation or download needed—original hardware runs it perfectly.