They get the date wrong; these were the departures on the evening of May 8. My guess is that they pulled up the Liveatc archives (and didn't credit Liveatc, in either the video or print stories) which are in "Zulu" time. Since these were evening flights on May 8, the "Zulu" archives are marked May 9, and I bet that made it through the reporting cycle.
Also, the article reports 400 ft vertical and 4200 ft lateral separation, but then says the aircraft "came within 400 feet of each other." Sloppy, but typical reporting, I suppose. Reporters don't think in 3-D, I guess.
Here's the associated audio clip from KIAH Tower, from the original file "KIAH-Twr-May-09-2014-0230Z", starting about the 9:10 point in that archive. Clip is about 4 min, starting from UAL601 ready to take the runway. This is an excerpt in real time, no edits (since it's pretty dense with communications already.)
Both aircraft report TCAS RA's; at 2:28 you can hear the male voice giving the "CLIMB" command in the background of UAL437's transmission.
Also note the controller is being very careful and clear with his departure instructions, e.g. for UAL601 before the takeoff clearance, he repeats the departure turn direction "right" and heading "340" twice each - no confusion here. But then, when he notices UAL601 in an unexpected (to him) position heading about 210, he tells them "you were given a right 340 heading", as if UAL601 had done something different. Well, yeah, isn't 210 right on a "long way around" right turn from 090 to 340 as cleared?