Well, this is a bit unexpected. Apple has rejected, apparently twice, the Steam Link app for iOS that would allow iPhone and Apple TV users to stream games from their Steam library to phones and devices. Weird.
Valve has issued a press release on the matter, and since it's a short one, I'll just paste the whole darn thing right here:
"On Monday, May 7th, Apple approved the Steam Link app for release. On Weds, May 9th, Valve released news of the app. The following morning, Apple revoked its approval citing business conflicts with app guidelines that had allegedly not been realized by the original review team. Valve appealed, explaining the Steam Link app simply functions as a LAN-based remote desktop similar to numerous remote desktop applications already available on the App Store. Ultimately, that appeal was denied leaving the Steam Link app for iOS blocked from release. The team here spent many hours on this project and the approval process, so we're clearly disappointed. But we hope Apple will reconsider in the future."
I tested the Steam Link app out recently, and it's been available for Android users for a full week. It's not entirely clear what Apple is objecting to, and I don't know what a 'business conflict' is beyond the fact that it sounds like guys in suits trying to hit each other with briefcases. As Valve's statement says, there are already a number of apps that stream desktops to phones (I tried one of those, too). I've sent an email to Valve for more details and I'll update this story if I hear back.