For us, it depends on your definition of work. I have 4.5 yo twins and started using some of the techniques when they were 3.5-ish. The things that helped me were; consciously setting my threshold for what is too much for me/the house (because then I had to be more consistent about stepping in), when it got above the threshold stating what it looked like was going on to me (gave me something to do other than yell knock it off) and expressing confidence that they would be able to come up with a solution that would make them both happy (rather guess -likely incorrectly 50% of the time - what was the issue to stay our of the middle of it; though sometimes I do offer suggestions if they're in a state in which the suggestion will be well received), and then separating if they continue to be fight (diffuses the moment and they usually come back with the problem forgotten or ready to compromise). Fighting isn't eliminated, but my reaction to it is better and their ability to come up with solutions is getting better all the time. Also, I pretty much use the book's method about tattling, though I often ask in a tattle if what they're telling me is a report (something dangerous is happening) or a tattle (they want to get someone in trouble) before responding and I don't think that was one of the books suggests.
I don't worry about bullying because I have equal opportunity aggressors. If one was dominant, I probably would, but I don't remember how the book addresses that as it isn't an issue for us.
In public I have other rules that would kick in about yelling before it came down to that they were fighting. We don't behave disruptively in public (store, restaurants, concerts, etc) as a matter of manners, so I'd deal with yelling at each other in those terms rather than as fighting. If they started up on a playground though, I'd treat it as I do at home.
But see, maybe I'm remembering the book incorrectly because I don't remember the suggestion of leave it alone until someone's at the risk of harm. My threshold is lower and when meanness creeps into the argument is when I step in.
A problem we had that the book didn't address for me was the lashing out in anger. We had a problem with implusive hitting, pinching, etc, with no pre-emptive arguemnt or warning for me. In those cases I'd separate, but it didn't seem to lessen the occurrence at all and I used other methods to help with that.
I do wonder about a 6 yo and a 2 yo old though because they're in such different places. I read the book when my dds were in their 2's but it didn't really make sense to me for them then; re-reeading at 3-ish it made more sense.