Parasite Eve 2 is basically Resident Evil +.
It has more weapons, more customization, more enemies, more skills, more environments, the like.
This sounds good on paper, but the problem with this is the "more enemies" part. Parasite Eve 2 uses the Resident Evil control scheme. In the earlier REs, enemies are easy to avoid and dodge, not so much in PE2, since they are faster and have a wider variety of attack types. The best part is that the game is actually challenging, especially on the higher difficulty levels.
That said, I love PE2 despite its flaws, but I'm also a huge early-RE fan. This definitely doesn't look PE2-ish.
As for why it's called The Third Birthday
The ending you get at the end of Parasite Eve isn't the "canon" ending. You need to reach the top of the Chrysler
building to get it. At the end of the Chrysler building, Aya's Mitochondrial powers weaken and go partially dormant from
lack of use, only to reawaken in PE2. That's why there are scenes in PE2 with Aya causing spontaneous combustion,
something only Eve could do in PE1. You'll notice during the scene before the game turns to "Night" that Aya goes into
her "Liberation" form, the final skill in first Parasite Eve and what would also be the equivalent of her being overtaken like
Melissa Pierce, but controlling herself rather than letting it control her.
Movie related, what I'm talking about is at 2:20
This one is better quality and doesn't glitch up like the above, but you have to wait until 9:00 or so to see it.
I'm assuming at the end of PE2 Aya's powers slowly go dormant again since she doesn't use them.
"The Third Birthday" means that they are going to be necessary for a third time.
Also, since someone asked yes, she is completely human. It's her mtDNA that was altered.