I was not aware it was released in that packaging, but I’m pretty sure that’s still a Playstation 1 disk dressed up in a PS2 style DVD case, meant to be used with the PS2’s backwards compatibility mode. To my knowledge SotN was never rereleased as a native PS2 title and wasn’t rereleased at all until the PSP version. (And then later the Xbox 360 and PS4 as downloadable titles, and also the ghastly mobile phone versions.) If you have a PS1 kicking around you can try it and see, I suppose.

For what it’s worth my copy is the green-stripe “Greatest Hits” reprinting, so what it’s worth is alas not much.