Interpolation is a guessing game where you take two frames as a reference. Let's call those ticks for clarity and we use those ticks to calculate and make assumptions.
The frames of reference was 0 movement in Linus test. Nothing have happened during the previous two ticks. The game has no reason to assume that he will move until the next tick. The next frame of reference arrives as a tick, the hammer have hit the mouse. 15.625ms have passed since the last tick. All the engine can see is that the mouse has moved. The engine decided to update the positions and we have no way of going back in time to redraw the screen. We can't get rid of this delay.
The game now have a tick where Linus is moving his mouse, the game may assume that Linus will continue to move his mouse until the next frame of reference. The game decides interpolate his movements and act accordingly. 15.625ms ms later and the next frame of reference arrives, the engine was correct! Linus is still moving his mouse and we may assume that he will continue to do so until we get a tick that says no.
Most professional players have given up on Valve and play exclusively on ESEA servers. They will tell you it's a night and day difference and that everything is a lot smoother. That is probably because ESEA servers have twice the tick-rate, 128 compared to 64.
Counter-strike players have since 1999 talked about rates and shared their configurations. Why do they do this? They want to take advantage of the extra positional data that you get from a 128 tick server. A frame-rate over 64 on a 64 tick server will only reduce screen tearing and the overall latency. You can't get more positional data then the server is sending you. The game can only assume that people will keep doing what they do and act accordingly, we call this interpolation.