And with only a few flowery lines from Sherlock? So vague, no threats. I don't see how he could actually have made Moriarty do anything - Moriarty had the gun after all! What could Sherlock have threatened him with? And we saw that Moriarty held up well to torture, so the threat of a beating wasn't the final straw.
Apologies if this has been discussed to death, I'm new and still looking around, but I was rewatching this scene, and the only way it makes any sense to me is if there are things they both knew that we were not party to, and which will be revealed in the next season.
The only thing that makes sense to me, if it was all just as it was and nothing more, is that Moriarty was so unhinged that Sherlock could take advantage of that, and use his volatility and the fact that he was so 'changeable' to agitate him into making a fatal mistake. But again, it just seems... not enough. This was a man who had his fingers in many impressive criminal pies, we saw throughout season 1 and 2 the kind of people he was dealing with - 'criminal web with a thousand threads and he knows exactly how each of them dances'. It does make me think that the two Moriarty's theory is possible - one logical mastermind, and one 'not wound too tight' showman - to be sacrificed when needed?