Seems like a strange way to end it. If they are beating an organized scourge attack, why can't they fight off a leaderless scourge? Unless it's supposed to be some sort of set up by Ner'zhul to regain control.
There are two theories.
One, while Arthas was an evil monster, deep down under all those layers of darkness was still a bit of good. This good side of him acted like a sort of leash, allowing him to sort of keep the Scourge under control. When they lose the master, they lose everything, including that one shred of good inside him, and thus the mindless undead lash out like a swarm of locusts. They have nothing holding them to any sort of organized effort, only random death.
Two, the whole thing was a plot by Ner'zhul to ensure his survival. He deep down influenced Arthas, realizing that he could not wrestle control of the body from the fallen prince, he instead deep down tricked him into grooming and corrupting a new host, Bolvar. When the time came close, Ner'zhul took the form of souls trapped in Frostmourne, and convinced the heroes that if the Lich King stays dead, the Scourge would destroy the world. The heroes believed this, and thus the events above. If Tirion had taken the helm, then Ner'zhul would have failed, thus Bolvar lashed out that only he could handle it as he was groomed to do. "It is my fate" as he would say. Now, Ner'zhul can try to regain control of his powers, by speaking with Bolvar in his dreams similar to how he did with Arthas in the years prior to WOTLK.
P.S. If you watch the video, you actually hear a progression of voices. First you have Bolvar's voice, then when he puts on the helmet his voice slowly shifts to the "Lich King's" voice, the one used by Arthas all through WOTLK. Then, after Bolvar is completely frozen in ice, a third disembodied voice appears and tells Tirion to leave, before finally mixing in with the first two voices. This third voice, if you listen to it while it is most clear, sounds like that of an orc, more then a human.