I used to play the guitar for a number of years. All you need for chord harmony is 3 notes, and 1 note for melody, so the uke can handle complex pieces like that guy is playing (and very well indeed). On guitar this is called 'chord melody' (which I used to be able to play). It's much like how a pianist plays, and is the original way the guitar was created to be played (in Spain).
Good for you Davy! I dabble in the guitar, chords only and only songs I like...I play only for my own entertainment as, I'm not one to get up in front of others...besides, I'm not very good but, I sure enjoy it! I could listen to Jake all day.