It happens in most of the sites I visit, and it's happend for the last months: two-fingers swipe to go back or forward don't work.
However, from time to time, there's some sites in which they work.
I have installed BetterTouchTool, which I thought might interfere, but I deactivated it and the same still happens.
Best Answer
I know I'm coming in pretty late but I too was facing this problem, so I thought I'll give the solution.
A hint - Don't use Chrome's in-built two finger swipe. I'm on Chrome 24 right now, so they've had ample opportunity to fix the problem since you reported it. But they haven't.
The problem actually is - web pages that are longer than the viewport and have content you have to scroll down to see will not work with the two finger swipe, the page will just slide up or down based on the direction you're pushing in.
The solution - use BetterTouchTool to define your own two finger swipes for Chrome. I did that and it started working instantly for Chrome. It works on all pages, regardless of whether they have scroll or not. I tested on a lot pf pages.
I know that this will not be as 'sexy' as Chrome's inbuilt swipe, but it works. You will also be dependent on BTT but I use it on so many apps that it remains on at all times.
I use BTT for three finger swipe in Finder to go back and forth and also for four finger tap to close a window (this works globally).
All the best!