Where did you read it? Also can I ask for spoilers? I wanted to know if her dad in the “game” her real dad? Like she was reborn into her first life again or something like that?
I heard from spoilers that she's the original Penelope so yeah he is her "dad"/ adoptive father
Spoilers regarding plot
As far as I remember, she was og Penelope. She has a power (there's more to it) and the only one who can stop Leila (acting Yvonne) from destroying their world. Vinter turns back time repeatedly to get to the path where Pene defeats Leila, but Pene doesn't know all about it (and that she has power or has to do something). Her personality has always been the same because of how people and her adoptive family treated her, so the future never changed. So every time her life repeats, she always suffered until her soul broke :( a piece of her soul reincarnated to her life in Korea, and it's brought back again to current story.
Read the novel, fucking cried my tears out.