I've listened to the RT on AvWeb and I suspect that the crew may not have had the capacity to appreciate the traffic situation during their departure.
That AVWEB "recording" is misleading. It's had at least 30 seconds edited out of the middle, from commencement of the 777 rolling until it gets to 500ft. Unless there was a traffic call during the time that is missing, the first thing either aircraft know about each other is when the controller mentions the 777 passing 500ft after takeoff (probably higher than that as the call was coming out). Had that call been made 5 seconds later and the lighty continued straight ahead through the centreline the TCAS would have been the only thing that would have saved all of them.
It is obvious that the whole situation was not planned and very nearly ended in major tears. Whether that was because of a mistake or a characteristic of the system remains to be seen. Either way, "much ado about nothing" is a rather odd conclusion to be drawn IMO.
What is also a worry is the UA captain asking for a discrete freq to talk to someone, I assume about the near-miss. At that point of the flight that
would be silly. Priorities...