Prior to 2.1.2 (I believe he was able to do this right before the patch. Smart man. No barb can catch him now)...
That's all you needed for a 2.1.1 Raekor barbarian.
Dust Eater Rift would be perfect because they're slow and their threat level is nonexistent. In addition, each are worth 0.75% progress.
You only need to kill 134 of them to spawn the Rift Guardian. Pure Dust Eater GRs exist. For a Raekor barb, that's like a child diving into a ball pit. I'm surprised it took him over 13 minutes to clear, which would lead me to believe that it wasn't as dense as it could be, it wasn't 100% pure Dust Eaters, or he didn't find a Conduit until he accidentally stumbled upon one after the RG spawned.
As for getting a GR60 key, the exploit revealed at the end of last week enabled many players to obtain abnormally high GR Keys. I personally still have GR61 Keys in my stash. It has since been hotfixed.
You didn't need a perfect rift, all you need is a Conduit Pylon. I watched Klankster doing several GR60 before the patch... he cleared some of them in 7-9 minutes (!), and then just spent 3 more minutes running to the end of the rift, spawning the guardian, and left. It was just about "who got the Conduit and on which level", depending on how many GR60 keys they had at their disposal. I don't know about Guspo, but since Klankster was streaming hours of his GR56-60 attempts I can tell that he was able to spawn the RG in many of them (actually the majority of the attempts I've watched he "cleared" in time, just got no Conduit).
So... the two words you're looking for are not "perfect rift", but "Conduit Pylon" ;-)
Thankfully it's over now. Time for the leaderboards to be cleared.