This looks like a variation of "stride piano", where bass notes are rhythmically alternated with chords some distance away.
Idiomatic stride piano is usually pretty technical due to the sheer velocity of playing -- you'd want to look up Fats Waller and Art Tatum as early pioneers of the style,and more recently people like McCoy Tyner and Hiromi Uehara have continued to push the boundaries of technique.
In the example you gave, the pianist is using the idea of alternating low and high left hand chords at a slow tempo as a way to get the best of both worlds -- deep bass presence, and lush chord voicing, in the context of "comping" for a singer. You'll notice that when he plays more than one note in the low octave, the chord is much more sparse or separated than it is when he plays in the middle octave -- this speaks to the tradeoff you have to make between chord density and positioning (a dense chord in the low octave is not going to sound very clean). In developing this technique, you'd want to start with just a single bass note alternating with middle-register chords at a slow tempo -- which is exactly what you'd be doing if you were practicing stride.