Except it's not. The video shows that. In the real world, the DAC doesn't immediately jump from code N to N+1; it slides (the "slew rate" of the opamp). More bits just makes the difference between codes N and N+1 smaller; i.e. where it slides to is more accurate to the original. The "stair step" or "straight line" view you get from programs like Audacity is a lie.