You're right. Subjugation of one state by another state does not equal imperialism. Imperialism is a specific phenomenon unique to global capitalism. I know a lot of Leninists will disagree with this, but in fact, one could argue that imperialism is not merely a stage of capitalism, but integral to it's existence as a global system. Thus imperialism can be defined as “precisely the amalgamation of the requirements and laws for the reproduction of capital; the social, national and international alliances that underlie them; and the political strategies employed by these alliances”. I'll just let Samir Amin explain further:

The modern global system of actually existing capitalism has always been polarizing by nature, through the very operation of what I call the ‘globalized law of value’, as distinct from the law of value tout court. In my analysis, therefore, polarization and imperialism are synonymous. I am not among those who reserve the term ‘imperialist’ for types of political behaviour designed to subjugate one nation to another – behaviour that can be found through the successive ages of the human story, associated with various modes of production and social organization. My analytic interest is anyway geared only to the imperialism of modern times, the product of the immanent logic of capitalist expansion.

In this sense, imperialism is not a stage of capitalism but the permanent feature of its global expansion, which since its earliest beginnings has always produced a polarization of wealth and power in favour of the core countries. The ‘monopolies’ enjoyed by the cores in their asymmetrical relations with the peripheries of the system define each of the successive phases in the history of the globalized imperialist system [...]

Imperialism, from its sixteenth-century origins to the Second World War, was a plural phenomenon; permanent, often violent, conflict between different imperialisms played an important role in shaping the world. In this respect, the Second World War ended with a major transformation, since a collective imperialism of the ‘triad’ (USA, Europe, Japan) then replaced the multiplicity of imperialisms.

• Samir Amin, Beyond US Hegemony? Assessing the Prospects for a Multipolar World