https://www.pcgamer.com/the-steam-link-app-could-be-closer-to-arriving-on-ios-after-both-apple-and-valve-make-changes/

While at E3, I got a notification on my phone that the Steam Link app on iOS had received an update. I still have a beta of the app on my iPhone from when I tested it prior to its release—a release that ultimately didn't happen because Apple rejected the Steam Link app for reasons that were a shade unclear. Currently, the app is only available for Android devices.

At the time, Valve stated that the Steam Link app, after initial approval by Apple, had been rejected due to 'business conflicts with app guidelines'. Valve wouldn't elaborate on the specifics, but it's becoming a bit more clear since Apple recently made changes to some of those guidelines. It now states that streaming and remote mirroring apps must limit transactions to the desktop host. Purchases can't be made through the streaming app itself.