Again, it's pretty clear that the "overshooting/Virgin" call was made by the crew of Alaska, and the replay "We're not overshooting" was from Virgin 345. There are two people in each craft.
The date is February 6, shortly before the original post was made -- you can find the recording in the archives. Alaska 382 and Virgin 345 both landed at 11:40 local, and this discussion happens at about 11:37. I pulled the paths from FlightAware, and have posted below the (smoothed) tracks. You can also type in AS382 and VX345 into FlightRadar24 and check the animations. Virgin was ahead of Alaska and heading for the right. Alaska was in a sweeping turn to the left, and about when VX345 crosses their path, they made the "overshooting" call; I'm betting on an optical illusion: they see the aircraft assigned to the right runway moving to the left of their cockpit window and assume he's on the wrong path. On the smoothed FlightAware track or the rough FR24 one, you can just see that Alaska flies the final minutes of the approach a little to the left of the centreline.
I see no reason for anyone to call for a go-around given the distance and clearance, and seeing as nobody did go around, I stand by my position that it's someone trying to police terminology.
The Alaska is angry because they think the Virgin is overshooting the right to land on 28L ahead of them.
If you pay attention to the voices, I think the voice that says "No, we're landing on 28L" and the redwood pilot voice is the same and it's just here when Alaska says "Nice job Captain" in a sarcastic tone like saying "Hey, you're getting ahead of me in my runway"
Now? When or what day this was? We could take a look to this both aircraft Alaska and VRD and see whay they did. Specially the VRD345.