Using the definition of the state as "a nation or territory considered as an organized political community under one government", can the Roman Empire, particularly of the late antiquity, be considered a state?
Why wouldn't it be considered one?
I know this is a problematic set of criteria, but it's what my university teaches its undergrads. A state has
Again, hugely problematic. But Rome fits those things.
The question I see more often (perhaps because of my research) is whether Rome can be considered a nation-state, and the consensus is that it can't be. There are a number of different theories about nation-states and nationalism, and almost all of them make nation-states things of modernity. People do argue about whether the state produces the nation (I think that's the direction Weber, Peasants into Frenchmen, takes) or whether nationalism produces nations (Benedict Anderson? I forgot who I read on Italian nationalism that argues this way).
There is a guy, Antony Smith, who argues that nations could and did exist in the ancient world. He picks Jews and Armenians for that. It's been a while since I looked at his stuff. I don't remember the Armenian argument very well. The Jewish argument had to do with the centrality of cult practice at Jerusalem (or lack thereof after 70 CE) - it provided an anchor in a shared imagined history linked with a homeland either currently or previously occupied and continuously remembered by a population that recognized itself.
Rome never got that. I would argue it came close with the Social War, Augustus' use of tota Italia, and some other similar things, but it never really sunk in.