When playing Quake over the net, the connection only has to synchronize the players positions etc. And Quake was pretty clever extrapolating the players motions, so even when packets were slow, they seemed to behave naturally. This frequently caused them to jump, when the positions were updated by real data.

With Stadia, the whole gaming graphics are streamed to your local client, so when the network is slow, the graphics will lag. And of course, it takes magnitudes more of data to transmit.