Do dishwashers with a built in "high loop" require a second high loop under the sink?
SUMMARY:

Reasons:


Building code may require you to follow manufacturer's installation instructions. Related to this, having a second loop under the sink could be easier to visually inspect/verify than the built-in one.
Apparently two loops is a safeguard against poor drainage. As such I think you might get away without having it but it appears to be a best practice to have two.




RESEARCH:

I found an article which discussed this specific issue and it included some manufacturer information.

Question posed to manufacturers:


  A high loop is required on the dishwasher drain in the installation
  instructions for all of your dishwashers. What is the purpose of this?
  Doesn’t the high loop that is incorporated in to the side of the
  dishwasher achieve the same thing?


IMO the single clearest answer addressed the specific benefits of a second loop:


  Viking: In testing our dishwashers, we have found that the additional high loop in the back of the dishwasher is required for
  proper draining of the water.  We have seen when this piece is not
  applied that over time the consumer will have issues with the water
  back up and causing issues with proper drainage and water pooling in a
  particular area.


Other answers reported were:


  Kenmore: "The high loop or air gap must be used to prevent potential backflow contamination of the dishwasher. Local plumbing codes
  generally dictate the requirements in your area. Section 807.4 of the
  Uniform Plumbing Code states: "No domestic dishwashing machine shall
  be directly connected to a drainage system or food waste disposer
  without the use of an approved dishwasher airgap fitting on the
  discharge side of the dishwashing machine. Listed airgaps shall be
  installed with the flood level (FL) marking at or above the flood
  level of the sink or drainboard, whichever is higher, or separately
  trapped with the airbreak located on the stand pipe."
  
  GE: "If an air gap is not required, the drain hose must have the high loop from the floor to prevent backflow of water into the
  dishwasher or water siphoning out during operation."
  
  Bosch: The high loop in the drain hose of your dishwasher is to keep water from settling in the hose if it were hanging down any lower or
  horizontally. This keeps the drain hose dried out and keeps any odors
  from backing up into the dishwasher.


None of these second group actually addressed the specific question of needing TWO loops, but they do explain why a loop is needed at all which is still useful context.