I think this is about military power.
I say thank goodness military might is not the only measure of power or we'd be in a sad state of affairs when you come to think of it. That's not to undersell the force projection of military might, and does not deny that the US (and Russia to a lesser extent) derive enjoy an outsized place on the world stage owing to military might.
Put it another way. You may be right but I do not want you to be right. I don't want to live in that world.
If you discount China as a superpower, then you discount a country that could single-handedly throw the entire world into a state of political, economic, and military chaos overnight.
Defining power as military-only is as naîve as defining it as male-only or violence-only or sword-only.
You are right. One should take care defining a word so narrowly that it can only apply to one thing. If "superpower" by definition means "characteristics only the USA has" then why not just call it "USA?"