Do search arbitrage pages have to label the ads as ads?
Yes. Sponsored search results must be clearly marked as ads, and search engines control how their ad units are labelled and styled. Adverts used to buy the traffic must also be recognisable as advertising. In the United States the Federal Trade Commission treats formats that disguise advertising as editorial content as potentially deceptive.
There are two disclosure points. On the traffic side, native ad disclosure rules expect a recommendation-widget or social advert to be identifiable as paid. On the page, ad disclosure means sponsored listings carry an "Ads" or "Sponsored" label and are not styled to look like navigation or organic results.
Feed rules restrict changes to the ad unit for this reason. A publisher who shrinks the label, matches ad colours to page content, or surrounds ads with arrows and prompts is steering people into accidental clicks. The engine sees the resulting poor conversion and responds. The FTC Act and similar laws elsewhere give regulators grounds to act where consumers are misled.