Playing PlayStation 2 games without physical discs is a popular way to preserve your console's laser and enjoy a faster, more organized library. While you can't technically "download" games directly onto a standard 8MB memory card due to their small size, you can use modern adapters and exploits like and MX4SIO to play games from an SD card inserted into your memory card slot . Core Requirements for Play via Memory Card Slot
To run games through the memory card port, you need a specific hardware and software setup: How To Make A Free McBoot Memory Card PS2 Guide how to download ps2 games on memory card