Gsync actively changes your refresh rate on your monitor to your FPS but it's limited to 30-120hz. People feel it's smoother because the picture he's talking about is in sync with every frame your GPU is putting out.
The reason it increases input lag is because of that cap at higher FPS. If you're pumping out higher than 120 then Gsync is effectively not working anymore and you get the same input lag that you get with vsync. Reason 1 why I abandoned it.
The basis of higher FPS being smoother and what he is saying is only the icing on the complicated cake. It's why on any online shooter playing PVP I turn all my settings down besides resolution, resolution scaling, and AA to get the highest FPS I can manage because yes, it is smoother. Gsync is only good when you're playing a game getting at 60 or lower. So for instance, when I had dual 980s and the ROG Swift I had Gsync on with The Witcher 3 because my fps was lower than 120 and it smoothed out the dip while avoiding screen tearing and input lag. On the other hand, playing Rocket League and Overwatch I stay at the FPS cap and never dip from it. When I turn one Titan X off and drop to about 175fps in Overwatch I CAN tell a difference.
There are two other variances he's not discussing which goes in the part of "why he can't explain it" and that's latency. The time it takes your click to the picture on the screen is one form of latency. Every thing in your machine including your screen adds latency. That's why "MLG 420blazeityoloswag gamerz" want a 1ms screen with the highest refresh. I personally don't play games like CS:GO that require this kind of ridiculousness. Another thing (which CS:GO has) that takes into account for how quick you are in FPS games is..you guess it more latency lol. Your ping to the server and round trip ping also plays a part in this. The server tick rate is also a remaining factor, and most all competitive FPS games have a server tick rate of 60 or higher. It's one thing to have your frame rate sky high, but if your ping to the server is high, your round trip to the server is high, or the time it takes the server to process this information is high it won't make much of a difference.
Finally the last thing he doesn't discuss because he probably doesn't understand it is frame time. Part of what he discussed was just that. There are articles that can explain it better than I can though.