Valve has had a very interesting relationship with gaming. While the company absolutely owns the PC gaming market, they have had no luck in branching out beyond the PC. The most famous issue was, of course, the Steam Machines. The company had hoped that building a Steam-powered Linux computer for the living room, they could challenge the dominance of Xbox and PlayStation. The brand was officially retired this year.
The company's most recent solution has been to embrace the trend of videogame streaming. If you have a Steam game on your PC, you can stream it to a number of other devices over your home network. Recently, the company announced that the capability was coming to Android and iOS devices through Steam Link. This would be a huge new feature for Steam, finally being able to expand its gaming dominance beyond the PC directly.
While the Android app is live right now on Google Play, Apple pulled the app from the App Store after initially approving the app. According to Valve,
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.
Apple's claim of business conflicts was believed to be because Steam Link did not abide by the in-app policy of giving 30% of purchase revenue to Apple. That theory was debunked, however, as Steam Link disables the in-app purchase capability, leaving that feature exclusively for PC-based Steam interactions. There is no explicit explanation given for the decision, but it is likely because Apple is working on their own game streaming service.
This would not be the first time Apple has denied an app because it either provided duplicated feature sets or because it conflicted with a business model that the company itself was working on. Apple famously denied the Google Voice app, because it duplicated features (especially texting). Within days, Google CEO Eric Schmidt left Apple's Board of Directors. They also denied a dictionary app because it contained all of the words in the English language.
Hopefully, Apple will get enough pressure from customers that they reverse their decision, as they eventually did with Google Voice or Ninjawords. For now, though, you might need to get an Android device to be able to stream games on the go.