starts at 2:08

How did this guy figure the key of the song while playing a bunch of chords over a 2-3 seconds of music

if i had to do it i would have to try identify chords over at least 20 seconds of music and say ok this chord is that one...this is that one...bla bla

how can he do it that way? how does that work

and how can he be sure its C minor that quick and not D# major

 

It's practice, experience and trained ear. With developed pitch, three chords with clear tonal functions are enough to know the key of song.