I actually hate games like I hate people who mug old ladies..or anyone for that matter...I dont play games because I cant be arsed with it..its far too much work for so little reward.
In answer to your question..actually its more of a statement than an answer...so sorry..but...I dont get where he is coming from..If you were the one to initially end it, or you had done something to instigate the break up then I could more understand why he might be umming and arring about getting back with you then getting shirty when your going out with someone else....is there anything you have not told us? Only reason I ask is because often people give one side of the story and its impossible to give a balanced view without knowing everthing.
Anyway, the other reason could be something that has been overlooked...something like, maybe he did break it up and realised he made a mistake, but after briefly getting back with you thought there was not the 'old spark' there so though maybe you were playing away so called it off again, thus making it 'your fault' in his eyes, then getting shirty after finding out you were seeing another bloke for a meal...which would have proved his point. There is no way of knowing this unless you sat or sit down and talk to him, with some blokes it is very hard to get emotional truths out from them, so make sure its the right setting to discuss these feelings.
The reason I have said all this is because its sometimes easy to give the 'expected' answer or the 'obvious' answers, but when it comes to matters of the heart there are so many possible answers we sometimes have to think outside the box for answers to do with affairs of the heart.
Hope it helps