And the Greeks fought with the Carthaginians, and with the Persians, and with the Greeks, and the Romans fought with...well, Romans, Greeks, Gauls, Germans, non-Gaul Celts, Iberians, Numidians, Carthaginians, Libyans, Egyptians, Persians, Hebrews, and, again for emphasis, the Romans. The Persians...well, you get my drift. The point is, all major Mediterranean empire engaged in warfare and were relatively good at it. Carthage is not in that regard unique,
So compared to that backdrop - the context in which Carthage existed - was Carthage particularly militaristic in any specific way? As in, did it stand out as more notably militaristic compared to these other civilizations? I would contend that it didn't. That's what I mean by "not particularly militaristic". That there was nothing particular - or unusual - about Carthage's military culture and achievements.
Rome, yes. Rome was absolutely, unquestionably a particularly militaristic civilization. War was central to their identity, to their sense of worship, to their political life. There's more to Rome than that (witness their Civ V iteration which is basically not militaristic at all), but militarism is a cornerstone of the Roman civilization. Mongolia, yes - conquering the largest continuous land empire in history in the space of three generations is actually particularly militaristic. It stands out. It's especially notable. That doesn' tmean they have to be pigeon-holed in that role, but it does mean that they are especially suited to being a militaristic civilization. Carthage is not on that level.
As to "trading hub is generic and boring", I could as easily say I find militaristic abilities generic and boring, and with about as much accuracy. But trade was far more important to who and what Carthage was than warfare, so between generic and boring options, we shoudl at least pick the one that's more descriptive.