Fun fact: In America, we have a term "summer fling" which is the same idea. Why anyone would want a short-term casual romance or a random hook-up over a long-term relationship is beyond me lol
Anyways, yeah, dude put himself in that spot. It's not cool to make jokes like that while in a serious relationship, and on a separate note, jokes are just harder to convey through text alone..
But, is it over-reacting to break up over a series of texts? Maybe, but the dude sounds like he has a history of bending the truth in his favor. Even if that wasn't the case, you said he tendency to talk about his dating life to you, in great detail too. Maybe it wasn't a joke to approach that other girl, after all? I certainly wouldn't trust his word on this lol
If he's not broken up over this and makes no effort to fix that relationship, then that girl might've made the right move in calling it quits tbh