They key part of a rout is that it is not simply a retreat but an utterly chaotic and disordered withdrawal, or even a shattering of cohesion entirely. It usually devolves into an every man for himself type attitude. This would then be contrasted with the opposing force who likely maintain morale and discipline and are therefor better equipped to inflict such grievous casualties that one can see during a rout. Also take note that a rout does not necessarily have to be over the course of a matter of minutes or hours. A routed army may have to flee for many days to find safety, vs. their enemy who has the leisure to chase them down at will.

Your Wikipedia source doesn't do the best job of explaining that those numbers for that battle are, essentially, made up and completely untrustworthy.

Routs had been pretty bad since well before the Romans, though. The Greeks in particular had such large and heavy bronze shields that dropping them was essential to surviving a rout: hence, the famous Spartan dictum to come back with your shield or on it.

You certainly understand that it's easier to kill people when they're running away and you're plunging things through their back. If you thought the armor helped, remember the grunts don't have much, are dropping their shields, and take off what else they have to run faster. If you thought they'd run faster that way—they do... but some people on the other side are on horses or (earlier) chariots and many others have bows.

/u/jarlaxle276 put it well. Basically, it's a lot easier to kill guys panicked and running away in chaos than it is when they're organized and fighting you.