The separation seems to good to be live. Especially with the 4 microphones that are seen. The vocals seem to be recorded in different environments.
Agreed. But I have some familiarity with this group, and I can say that they wouldn't "fake" anything for a video that they couldn't actually perform.
In other words, while this video might have been "optimized" for the viewing public, these folks can and do play this song in this manner...