No, it doesn't. The client receives the video + audio and sends control inputs to the server. The game data doesn't touch the client device.
It's the same concept as RDP and VNC. With fiber being rolled out in more and more places, input lag will become a thing of the past.
Source: I used to be a VDI Engineer. I designed and maintained the infrastructure for 1k zero clients that had lower specs than a Pi 3.