They also have their own index. But in any case, what matters here is the product UX itself not the internal details, and they do offer a classic search experience
Until you realize that Kagi only works well because it uses a (paid) third-party API which behind the scenes does a classic Google search, scrapes its results in real time, throws out the ads, and then returns the cleaned-up results.
If Google Search changes, then Kagi's search will be impacted directly.