Eh, I think state extracting surplus value from internalized othered societies (like roman or ottoman empire) fits empire implication, as well as a state working through sanctions/bribes on other states. But maybe I should workshop this a little bit in my head .

Workshop broke, so I’ll just put my thoughts:

From marxist lens, state is an arm of the bourgeoisie to facilitate transfer of surplus value in centralized manner, with understandable logic and stability(tm), i.e. rule of law and centralized violence machine (police and army). As such, empire is just extension of this logic outside of state borders/existing society to facilitate this transfer on the otherwise unoccupied states/societies.

Now, every colonial power in history and america should fit our future working definition, while satellites (like singapore or norway, which are not directly engaged in building of the empire, but benefit from unequal exchanges nevertheless) should not. So we take extraction part and add the threat part.

Society part i think is important delineation for our definition, as internalized othered societies (like indigenous and other marginalized groups in usa/france, gauls/later germans in Roman empire, christians in ottoman empire, Jews and myriad other groups in russian empire) do not benefit or even has control over empire in any shape or form, as they are not part of the ruling bourgeoisie of empire’s society, by property right restrictions usually. But they have their own bourgeoisie and working class, they just operate as separate, subjugated entity.