But aren't Khan and Marcus' views subjective? Given that, as you said, Marcus wanted a "proper military", and that Starfleet is certainly the governmental organization that would have to deal with the Klingons, doesn't that tell us that they are indeed a military organization, just one that is more varied in purpose and perhaps overstocked with scientists?
Which is kinda my point in the post above: the whole point of having a professional military is having a dedicated organization whose job it is to defend the homeland from external threats. For historical and political reasons, that organization is tightly controlled and has a lot of limits on what it can and cannot do, and when and where. This distinguishes military organizations from, say, law enforcement, privateers, mercenaries and local militias. It's not the mission role that defines it, but the nature of the organization used to fill that role.
Starfleet is a whole different animal. To begin with, the Federation doesn't seem to CARE who defends its interests, they'll send anyone they think can get the job done. They also have extremely lax controls over what Starfleet does and to whom, the only real restriction being a blanket prohibition on interfering in the affairs of pre-warp civilizations or the internal politics of foreign governments. It's an entity that can do many things traditionally done by other types of organizations, but Starfleet's FOUNDING goal is the exploration of space, and therefore it is, by definition, a space exploration agency. It's ability to participate in war doesn't make it a military organization any more than its ability to arrest criminals makes it a police force; going by mission roles alone, the mission on Nibiru would otherwise suggest that Starfleet is the galaxy's most powerful fire department.
Marcus, on the other hand, wants to transform Starfleet into a full military organization that specializes primarily in combat and warfare. Again, such an organization would be able to fulfill a wide variety of roles, but the political and legal and eventually even MORAL implications of that would be quite troublesome in the long run. Starfleet would have to change fundamentally the way it does ALOT of things, and also change the kinds of things it is and isn't allowed to do.