What you say is true only under the assumption that all states will function as rational actors which they rarely do in real life. And the economic objectives of America and China are "vague" only in the sense that they don't come right out and say what they intend to do because there would always be major backlash from local populations. But when I say "taking over territory" I am referring to economic domination. That's how modern imperialism works. You force another country's economy to be so tied up with yours that they cannot safely risk resisting any demands you and your business interests make. It also helps to place military bases in said country which the US has done. The US maintains a fairly aggressive military presence in Asia. Not aggressive in the sense that it attacks but in the sense that every country in the East knows it is capable of it. These two factors are what would worry China or any other economy that wishes to remain as free as possible from America's influence.
And the "too capitalist for war" argument does not hold up historically. Both World Wars were fought between Capitalist countries (Soviet exception). Capitalist economies must inherently expand to keep up profit increase. A century ago, there was really only one dominate capitalist force: the Us and Europe (excluding the capitalist tendencies of the USSR before and after Stalin). Now, there are two rival capitalist factions: the US, Europe, and NATO in one group and the BRICs countries in the other. China and the US enjoy a very lucrative partnership but one that has always been tense and only one bad incident from war. They are our biggest economic rival and will be for decades to come. I'm not sure what you think most wars are fought over, but I can confidently say that it is usually profit.
Once again, war seems unlikely simply because their hasn't been one on this scale in a long time. If current tensions, history, and foreign meddling (US) are brought into the mix, it becomes far more difficult I believe to simply brush off the concerns (especially with the polls mentioned in the article). And if we throw in political and social unrest both countries are increasingly experiencing, the whole situation becomes even harder to predict. It's hard to believe that the US will simply sit by and watch as it loses it's unprecedented economic hegemony or that China would be content with second place.