Games for sale meet the following conditions
New game refers to a game that has never been opened. There is typically a seal that is unbroken on the case or box. There can also be a sealed shrink wrapping around the packaging. This can refer to a brand new title or what's called new old stock, which refers to an old game (retro or vintage) that has remained in new condition because it has never been opened.
Pre-Owned game refers to a game that has previously been opened.
Neither of these conditions affect the rating of the game accept that a new unopened game is assumed to have 5/5 rated contents, considering it's never been exposed.
It's possible for a new game to have less than a 5/5 outer package, especially if it's old stock.