While Chase does make a fair amount on interest charges and various fees, I'd say that the rewards are pretty much entirely paid for by a combination of swipe fees and most people simply not using all of the benefits. (Remember how debit card rewards pretty much went away a few years ago after swipe fees for those were capped to almost nothing?) If everyone used their CSRs only for travel and dining expenses for instance and transferred their points to airlines instead of using Chase's portal or not using them, the card would likely be way less profitable.
On that note, I'm betting those fees will be capped for credit cards at some point as well--the chip transition in the US has basically restarted the merchant fee fight again, and this time customers might actually side with the retailers due to how badly the transition has gone. They probably won't be capped nearly as low as for debit cards, but the rewards will probably still be nerfed to some extent.