I don't love that new Bowie track, but I like it well enough, which is why I'm glad there's a like button as opposed to a love button. Well pardon me, there is a love button, it's just that we don't have one readily accessible here. There's nothing really atonal about that track at all. The backbone is largely in Major keys, but the auditory complexity is the change from E Major to G Major. So it sounds more complicated than it is.
Bowie also treats these chords as IV chords rather than as I chords, which creates a sense of drifting in no defined key (in other words, the E Major chord is not I of E Major, it's IV of B Major and the G Major is not I of G Major, it's IV of D Major - this approaches changes the scale used to a Lydian mode - I'll leave it at that, unless you are truly interested in more). He also bases key aspects of the vocals on non-chord tones, which further assaults the ear to the point of wondering what's going on. We are used to hearing music lie naturally in a key, even as the keys change. In this one, his vocal confuses the ear through the selection of chordal (key) centers and note choices for the vocals.
I played along with it a few times and his vocal intonation is pretty much spot-on. Whether one likes this track and the jazz-like approach to both the instrumentation and the use of modes, is another story.