The guitars are arguably out of tune/tuning.
Makes the chords feel like jangly, ill-fitting clothes, even with the lead being flat.
Reminds me of The Doors and many John Peel live sessions.
Deliberate artistic effect? Certainly makes me feel tense.
Haven’t seen this, but count me as a fan of anything that has Kelly Macdonald within. 
Some folks go to the heart of the matter.
Personally, I dislike pianos for semi-permanently compromised tuning (it shimmers), and the sound of felt hammers. Strings are better for plucking or caressing, not hitting.
Naming it and hitting it are two different things.
Vocalists are unconstrained by fretting about the instrument. Thus the chords have a ‘proper’ geometry.
All part of the mix, or something you notice?