What is the advantage of using a railgun over a hypersonic missile? Maybe cost, since even if they destroy their rails I assume those are cheaper to replace than a whole rocket?

Yea, cost. It was supposed to be installed on the Zumwalt, with a guided 155mm cannon as an interim, also with the goal to be cheaper than missiles. Unfortunately both ended up being more expensive than missiles. Replacing the rails isn't something that can be done quickly or cheaply.

It is kinda comparable to hypersonic missiles in that it can penetrate air defense, but that is about the only overlap, the railgun is long range for a gun, but nothing compared to something like a hypersonic missile.

From the article: "As railguns use electricity instead of explosive force, their projectiles are considered more durable and safer to store."