Not strictly necessary. If his parents were US citizens–and they aren’t–then it wouldn’t matter where he was born. Kind of. I think that there might be residency requirements for children of US citizens that are born abroad, e.g., if your parents are expats and you live all your life in another country, you might not be a citizen, but it’s complicated. You’d def. want to contact an immigration attorney if that was the case.

BUT…!

The point is that Musk, since he wasn’t born to US citizens, and since he wasn’t born in the US, isn’t eligible to run for president.

It’s an open question as to what happens if he ran anyways, and how votes would be tabulated, etc. It would get messy, but I don’t think that it’s ever happened that someone ineligible has run for president and won any significant amount of the vote.