A rigid chain of command doesn't make a military either. Besides, we're thinking about this from OUR point of view, in the country that borrowed a lot of legal traditions and concepts from 18th century England including the preference for tight civilian control of a large professional fighting force (via the Magna Carta). In other parts of the world -- even countries that aren't ruled by juntas -- the military is sometimes a state within a state and actually has political power of its own that the government has to respect if they want to get anything done (or stay in power at all); this is almost a modernized "warrior caste" as a distinct political bloc with its own interests. And on the far opposite extreme from us, we have militaries that are ruled directly by self-appointed dictators, sometimes where said dictator is himself a high level official OF the military. The Federation has a superficial resemblance to the United States, but is otherwise a completely alien society. Consider the possibility that civilian control of Starfleet is actually a lot less strict than we expect it is, that Starfleet's standing is more similar to, say, Imperial Japan or Egypt in which its military is a semi-independent society in its own right that is parallel but not entirely subordinate to the Federation government. Classifying themselves as a non-military organization might be the result of their surrendering certain military authorities in exchange for the Federation continuing to leave them to their own devices. They featured prominently in Enterprise; Travis Mayweather, particularly, was born and raised on a long-haul interstellar merchant vessel before joining Starfleet and becoming the Enterprise's helmsman. It's directly implied the ECS actually traveled quite a bit deeper into space than Starfleet had at the time of the NX-01 mission; Travis was essentially the only person on the ship with any deep space experience. Interestingly, the Earth Cargo ships of that era were armed with plasma cannons, and the first time we see them one of their captains is (ineptly) attempting a military assault on a pirate anchorage and has to be rescued by the better armed (and also non-military) Enterprise. Which illustates my point: a Jem'hadar "fighter" is a small starship in its own right, complete with a bridge, an engine room, cargo bays, and a crew of twenty to thirty. They are comparable in size to the Klingon bird of prey or the Maquis raider, with the firepower of the former and the agility of the latter. Think of the Pegasus class hydrofoils: a ship large enough to mount warship-grade offensive weapons but small enough and fast enough that it can literally run circles around its target and dodge return fire. They can if they have an engineer on board. That kinda works in TNG, to a certain extent -- with the very troublesome fact that we've never seen the Picard maneuver or anything like it ever used again -- but it doesn't fit well with NuTrek or post-TNG depictions where combat ALWAYS takes place at sublight and warp drive is only used to get from one battlefield to another (or where combat is possible between co-moving ships at warp speed and relative motion is almost zero). Significantly, the Romulan fighters on the Scimitar do not appear to be equipped with warp drive. More significantly, the Scimitar never launches any of them during the fight with Enterprise. These two combined indicate that at least Romulan fighters are not useful in ship-to-ship combat.