Well, as long as that device is not an iPhone, that is. You'll find that it's pretty hard to find a cloud gaming app on the App Store and today, another popular one — Shadow — bit the dust.
As announced by its developers, Shadow was removed from the App Store for not acting "in accordance" with the guidelines. So far, it hasn't been revealed which part of the guidelines, but Shadow developers did say they will be looking into ways to fix the problem.
Actually, it's not the service itself that Apple finds offensive. You will find that there are plenty of personal game streaming apps that you can still use — like Steam Link, which lets you remotely activate your personal computer at home and use it to play your own games over the web. So remote gaming is a-OK by App Store standards.
However, cloud gaming services usually connect you to a store where you can buy the titles you want to play. Technically, these are in-app purchases, which you make in a 3rd party store. So, Apple can't take its 30% cut from these in-app purchases. As per App Store guidelines, this is a big no-no. Even Steam had huge problems with this in the past, but has somehow managed to fix the problem.
That's not to say this is what happened to Shadow. But the situation does seem entirely too familiar.
Some might be thinking that Apple is banning cloud gaming services because it wants to promote Apple Arcade or because it plans on launching its own game-streaming service. This isn't outside of Apple's MO, but we doubt that Cupertino is thinking about launching cloud gaming any time soon. It's pretty far from the company's expertise or focus right now.