All modern GPUs have isolated memory contexts and full CPU-like virtual memory address space and page tables for each user context. It's not possible to (directly) read data from another context. As far as I can tell from what you're trying to say, your comment is completely incorrect about GPUs not supporting that.

From the description given, I assume this is using timing differences to tell the size of each compressed tile, which gives you info on it's contents. This is certainly not helped by the ability for an apparently untrusted iframe to apply a transform to a target that the security model would normally disallow reading pixels from, amplifying the data from this side channel. Without that it's "just" another sidechannel attack.