A political unit having an extensive territory or comprising a number of territories or nations and ruled by a single supreme authority.

For this definition to hold, the US would have to be directly ruling other non-US nations. So far as I understand the definition, that means the US's laws would apply to other nations; other nations would be required to pay the US taxes; things of that sort. This isn't the case.

The dominion of an emperor; the territory or countries under the jurisdiction and dominion of an emperor (rarely of a king), usually of greater extent than a kingdom, always comprising a variety in the nationality of, or the forms of administration in, constituent and subordinate portions; as, the Austrian empire.

In this case, an emperor (which the US doesn't have) would have to be the ruler of a number of nations (which isn't the case). Importantly, those nations comprise "a variety in nationality". This is common sense. If for example the US conquered Mexico and added it to the US, that's be an empire, because Mexico is of different nationality than the US. China for example conquered Tibet and made it part of China; I think you could argue that China is empire-like.

But it's a grey area, at some point. If China says "Tibet is part of China", and Tibet says "We're our own country", who's right? Beats me.