Tons of good stuff here.
The first thing you notice about the GS offense is that the guys that can shoot are always spacing the floor for each other.
In almost every clip, you see Thompson and either Barnes or Iguodala in the corner, dragging their man away from the action at the top of the key. If you help off either corner, you are immediately hurt with either an open three or a drive off the pump fake.
Golden State creates what is known as gravity. Their shooters keep defenders close because you can't give any of them open looks. Selden, Greene and Svi can do the same for KU.
The other thing that really stands out is that there is rarely a post man in Golden State's offense. The lane stays open, even when Bogut is on the floor. Golden State wants the lane free so that when a guy rolls on a screen, there is no defender waiting in the lane. There's some nifty action around the 3:30 mark in the video where Bogut, Livingston and Green are all up high working a screen weave set. Curry and Thompson (the only two classic "shooters" on the floor) are spaced to the corners, meaning every defender is at least 15 feet away from the basket. Bogut sets a down screen for Curry and the entire defense breaks down. Everybody runs to guard the most dangerous man on a basketball floor right now (Steph Curry running to the three point line) and nobody goes with Bogut as he slips the screen. The threat of the three gives Golden State an easy lob for a layup.
In fact, as you watch the video, you see Golden State score inside fairly often, but instead of scoring on post ups, they score on lobs, back door cuts, straight line drives, and fast breaks.
The crazy thing is that KU already runs some of the same stuff that Golden State runs. Golden State runs a high weave (seen from about 4:45 to 5:15). KU runs that same action. The only modification is that Golden State runs it on an arc, while KU runs it flat.
Golden State runs the high pick and roll between the circles (a basketball staple. The difference is that they raise their other post man to clear the lane for the roller, while KU spaces the other post player to the short wing sometimes. By raising both posts and putting shooters in the corners, Golden State clears the lane for backcuts by the shooters on overplays or rolls by their big men (particularly Bogut and Ezeli).
GS also screens a lot with their wing shooters screening for their bigs. They get tons of layups and dunks when a big man gets caught "in between", not sure whether to stay out and challenge the shooter (typically Curry, Barnes or Thompson) or stay on the big man as he pops out (typically this is Green). KU could do the same with Greene and Svi screening for either Ellis or Bragg, both of whom can handle the ball and hit jumpers.
Golden State forces defenders into impossible decisions. Because they keep the floor spread with shooters you either help and deal with the open threes or give up layups. For most teams this year, neither option has worked.