What the article means is that if you have a single, very short emission of waves with a combination of multiple frequencies, then in principle an observer ought to observe all of the emitted waves arrive at the same time, regardless of frequency. (Traveling the same distance at the same velocity should mean arrival at the same time, after all.)
In this case, though, they see the radio-frequency equivalent of a short blue flash first and later a short green flash and then a short red flash (and presumably all gradations in between, all blurred into one event of gradually decreasing frequency). The notion (as I understand it: not my specialty) is that the longer wavelengths get slowed down a bit more as they pass through galactic and/or intergalactic dust, so their speed is lower.
Now, what you're probably wondering is, "Why do they think it's a single short event that's gotten 'smeared out' during travel rather than a longer event that continuously changed wavelengths as it happened at the source?" I don't know the answer for sure, but astronomers have a lot of practice in recognizing these things. One possibility is pulse shape: if the pattern of brightening and dimming of the "blue" light looks exactly the same as the patterns for the "green" and "red" light, it's more likely that it came from a single source event rather than a continuous process.