I never noticed that about Riker before, but now it's all I'm going to think about the next time I see a TNG episode. It's so bizarre.
I wonder if there might be some production reason behind it? Like they had all the camera angles set and didn't want him to move the chair out of place? Seems unlikely, since we never saw anyone else doing this that I recall (of course, I was never looking for it before now). Could be related to how tall he is and the camera angles involved in that, though. Weird.
Now we've got a new drinking game when watching TNG.