That's not what's happening here. The attack is exploiting a side channel of the rendering behavior, not reading the screen. There's no particular reason to believe that iOS is immune to something like this, though certainly no claim has been made. It's a new idea, it'll take a while for people to puzzle through the implications.
How are you sure? This isn't abusing some poorly secured screenshot API, this is a timing attack on the GPU rendering process and impacts a wide range of GPUs.
This attack measures the time needed to draw each pixel which varies due to graphical data compression. It is based on the "GPU.zip" vulnerability which was shown to affect most modern GPUs, including from Apple.