Only 15 of the 27 EU states use the euro - the UK, for instance, doesn't.
The EU states retain their own sovereignty (and therefore military), but functionally they're pretty similar to the United States. That is, for most practical purposes, the EU can be viewed as a single country. The linked article is only referring to the economy (or that part that uses the euro, the so-called Eurozone), which is definitely a single entity when compared to the US.
The US has 300 million people in 50 states, all of which use the dollar.
The Eurozone has 317 million people in 15 states (mainly France, Germany, Italy and Spain) that use the euro.
Looking at comparitive GDP from 2006, it appears that the US economy has lost nearly one fifth of its value since 2006 (the Eurozone's also grew a few percent).
Six years ago, the US dollar was worth 1.13 euro
Five years ago, the dollar was worth 0.93 euro
Four years ago, the dollar was worth 0.82 euro
Three years ago, the dollar was worth 0.75 euro
Two years ago, the dollar rebounded to 0.83 euro
One year ago, the dollar was worth 0.75 euro
Today, the US dollar is worth 0.64 euro
That's a reduction of 43% in six years, hardly surprising given the massive trade imbalance. I reckon 0.60 euro isn't too far away.
BTW, as the 51st or 52nd state, Australia isn't necessarily in that much better a position, so don't get the idea that we're gloating or anything.