Hi Uffe!
The track you linked doesn’t sound like it contains western harmony functional chords inside. I’m hearing trills between half-step notes and an occasional whole-step note to make the tension ramp.
However, to answer your question, the method I use to determine chords when listening to arpeggios is to listen for the lowest note and then work out what the interval is between it and the closest note to it, then do the same for the next note. The relationship between the intervals will usually give you the biggest clue to the chord.
Sometimes there can be multiple chords being outlined during a single arpeggiated melodic line. It’s not always easy to pick out when this is happening, though one trick for that is to listen to the harmony/support instruments and if the notes shift under a particular spot in the melody, it’s highly likely that the chord has changed