Regarding Chess, within theore of the Barbie movie all Barbies are Barbie. I don't want to spoil much (not that it is major) but they refer to each other as Barbie in the trailer so that feels like a safe thing to mention. So presumably there's a Grandmaster Barbie somewhere who would beat Oppenheimer. But if it's just Oppenheimer versus the main Barbie (Margot Robbie's) then I don't know because I don't know if Oppenheimer played Chess.
I think the real question is could Oppenheimer get laid by Barbie. Now, I know what you're thinking, what the hell? Here's the thing. The protagonist Barbie is not very interested in Ken so she's not very sexualized (well, at least in the sense of having sex). Meanwhile, somewhat surprisingly, Oppenheimer was quite a ladies man. He had a communist mistress. So the question of would they end up together is not that far fetched of a question.