It only applies, I think, if he gets the nomination or is chosen for the VP slot.
I don’t think either will happen. He’ll make a run for the nomination, but his views are looking more and more like his Dad’s and he’s had a number of high profile tripups. He won’t be able to obtain it.
Wouldn't it also count for primaries? I assume Kentucky has one and Paul would have to be on there twice if he was running for both president and reelection to the Senate.
But primary aside, say through some miracle he does win the nomination or is chosen for the second spot on the ticket. It appears like he still intends to run for his senate seat on the chance that he doesn't win the other election. That's where the Kentucky law appears to trip him up.