The Dominion insignia flashed on the screen and Jake raised an eyebrow in surprise. Ever since they'd had their butts handed to them on a platter, the Terran Dominion had been somewhat less than dominating.
Continuity issues abound, making the fan's head spin. And for the person who isn't familiar with Starcraft, this is bound to make them feel like they missed out.
The Terran Dominion is a collection of several planets, all ruled by Mengsk. Sure, in Brood War the main world Korhal was taken out by both the UED and the Zerg, that by no means is the entire Dominion. They're not a tiny enough group for "having their butts handed to them" to not have extremely serious consequences for all of humanity in the K Sector. Keep in mind that even third person is told from a character's perspective, and someone neck-deep in archaeology wouldn't likely know the real story behind the events of Brood War, especially since Mengsk is extremely secretive.
Also, it's pretty cheesy to say "their butts were handed to them" outside of dialogue from a character who would say something like that. It's not a good way of communicating information to a reader, besides being a cliche.