While Aereo was shut down for reselling OTA TV service over the web, AirTV shouldn't pose any problem for Sling TV. You're relying on your own antenna, after all - the box simply streams a signal that's legally accessible to any private consumer. It's unclear how the OTA channels will integrate into Sling TV's channel guide, but hopefully they won't seem too out of place.
Sling TV previously bundled OTA antennas with its service, with the hope that customers would access local channels outside of the Sling app. The AirTV box is the logical next step, giving you a way to view those channels anywhere you can access Sling TV. Sources tell Zats Not Funny that the company is working on several new devices. It looks like the AirTV can only capture and spit TV signals over the internet, so it's not hard to imagine another box that can also be plugged into a TV and serve as a standalone Sling TV solution.
While Sling won't have to worry about licensing channels with AirTV, its mere existence may cause some friction with its broadcast network relationships. And of course, OTA reception varies wildly depending on where you live and the quality of your antenna. AirTV likely won't be as easy to set up as Aereo, but it might just be what many cord cutters need.