I just asked this question on RacketBoy because I'm trying to play Shadowrun Returns on iOS. Here's what I found out so far.
If you already downloaded Shadowrun Returns with your iTunes account back when it was available, you can still download it with that same account on older devices.
However, even on older devices, if you didn't download the app/game before it was delisted, you can't find it on the App Store. I've tried on an iPad 2, 3, and 4.
I don't know where to download the Shadowrun Returns package, or if that's even possible. However, if I could, I think the only route is to jailbreak the older device and then install it. This doesn't help you because you want to play on newer hardware.
I never fully understood the appeal of physical releases or fully appreciated the freedom of Android sideloading until now. Though even with Android sideloading, I'm not sure how I would register the game. Maybe developers could set up a donation page where we can send them a few bucks when we want to play their unsupported games.