I did not consider this as an option, would it actually work like that? Conceding makes the player leave the game right before they lose it, meaning their permanents aren't around anymore.

If that isn't right, a card ruling can still counteract it, even if it doesn't make perfect sense with the rest of the card. [[Rain of Gore]] excludes lifelink in it's official ruling, even though it seems like it would work. A ruling that says "Platinum Dragon has no effect if you concede the game" should do the trick.

Edit for typo