You misunderstood the parent comment. They were saying if the law changed then the US presidential election (or frontrunners if they compete in the primaries) would be Arnold vs Elon.
Meanwhile, Elon could not run against Arnold for governor of California: Elon is not a citizen of California and Arnold has been disqualified from running again since 2011 due to term limits.
All US states have citizenship. It cannot be denied to any US citizen. Basically, it determines which state you get to vote in and what state you primarily owe income taxes on. In California it's automatic if you are a US citizen who primarily lives there for 3 months with no clear indicator you plan to move on. The process is similar, but the amount of time is variable, between the states.
It can get tricky and people (or states) can argue/sue about it because it can make a big difference in taxes. Elon became a citizen of Texas before he made all the money that resulted in his 11 billion dollar federal tax bill last year and in doing so probably saved himself 5 to 7 billion dollars that otherwise would have gone to California.
