No, they just pay for their APIs per search. It costs Kagi about 1¼¢ per search.[1] Each user searches 20 times per day on average.[2] So it costs Kagi $7.50/month just to physically provide one person with search results, ignoring any overhead like buildings and employees. To keep the lights on they have to charge at least more than that.
[1]: https://blog.kagi.com/status-update-first-three-months#finan...
[2]: https://kagi.com/stats
