Hi Leo
Without doing an indepth study on the video this is what I'm seeing and hearing:
First of all video and your piece are 2 different styles but ignoring that...
She's finger picking, a Fender bass and either through technique or eq not a lot of mids.
Kick drum - probably a felt beater, close mic'd, there's padding (dampening like a pillow) in the drum* - no ring, flap or room tone. Played firmly but not hard - again not a lot in the mid's.
*or they ran it through an envelope follower to remove all ring & sustain.
For most of the song kick pattern is simple, sparse and whenever he hits the kick - she's on it, every note.
Towards 3:40 you can hear some kick with out bass on top and it's not your topical rock kick.
When the kick & bass play together the bass notes get emphasized almost like she switched to using a pick for those notes.
Your kick - little or no dampening so heads are a lot more ringy, some kick in the room sound or vice versa, harder beater or your velocity is set high enough to be clickier.
Bass & kick may be dating but they're not married. Even if you had the bass & drums sounding the same as the video it wouldn't feel the same, they're a lot more busy and they're not in playing in sync enough.
Anyway here's you 5 minute opinion - YMMV, hope it helps.
Best regards,
...Steven