I think you're right. Suppose the connection to the game streaming service adds two frames of latency, and the player is playing an FPS. One thing game engines could do is provide the game UI and the "3D world view" as separate framebuffers. Then, when moving the mouse on the client, the software could translate the 3D world view instantly for the next two frames that came from the server but are from before the user having moved their mouse.

VR games already do something like this, so that when a game runs at below the maximum FPS of the VR headset, it can still respond to your head movements. It's not perfect because there's no parallax and it can't show anything for the region that was previously outside of your field of view, but it still makes a huge difference. (Of course, it's more important for VR because without doing this, any lag spike in a game would instantly induce motion sickness in the player. And if they wanted to, parallax could be faked using a depth map)

You can do parallax if you use the depth buffer.