Well, when Chrome first came out, it was definitely way faster than the other browsers for websites that had heavy JavaScript usage a la GMail. I imagine the gap has closed quite a bit, but I would suspect that it's probably still there, since they can coordinate development of both their web apps and the browser to work well together.
More recently, there was that whole thing where YouTube was "accidentally" adding delays to non-Chrome browsers.
I think it's more that everyone used Google for search (because it at least was legitimately the best by a good margin) and then Google used that position to push Chrome. The other stuff may have helped, but I think search was 90% of it.