I’ve always wondered the answer to that question myself. A developer like Square-Enix isn’t dumb enough to intentionally drop the title and confuse fans as to what exactly this game represents.
Turns out that Square-Enix don’t own the full rights to the series. Did you know that the original PS1 classic is based off a best-selling Japanese thriller novel? Weird, eh? Thankfully, Square-Enix is looking to to renew whatever license fees they need to pay in order to revitalize the franchise once more. Deals like this take a longer than expected, which is why they’re having difficulty in bringing the PS1 classics for download on PSN. Smart of them to pursue doing so, however. In order to secure a solid future for The 3rd Birthday and whatever sequels they’re planning on making, you need to expose the original games to the masses. Personally, I would love to play Parasite Eve 2 again. I remember enjoying it a lot more than the first game due to it’s fast-paced nature and lack of RPG sluggishness. While the first PE wasn’t bad, I didn’t really appreciate the survival-horror vibe because it played more like an RPG. PE2, however, is more RE-oriented.