What is "HDPLA", and why is it so hard to find out more about it?
So, low-teck, old-style investigative work from my side.... I contacted a company selling HDPLA and they got back to me with the following reply.


  We created HDPLA as an industrial PLA with special additives. As a result, our so called HDPLA has the advantages of ABS, but prints as easy as regular PLA.  HDPLA has high impact, high strength and high heat deflection temperature (hdt). You can also print at high speed (max 140mm/s inhouse tests).  HDPLA has is own high strength, but is even more strong after annealing.  A heated bed is not necessary (50-60˚C recommended), and you can print with HDPLA with a 3D printer with open structure.


This is strikingly similar to the description of what 3Dprima calls "Prima SELECT PRO":


  PrimaSelect™ PLA PRO ist the next generation of high performance PLA for demanding industrial applications. Designed to be able to print fast >120mm/s so you can save on production time. Very high heat resistance (95°C+) after annealing. Excellent mechanical properties combined with a matte surface finish that helps concealing the printed layers for optimum appearance.


While writing this answer I also found a page that escaped my googling until now, sating an additional property of "their" HDPLA: food safety.


  With our HD PLA you have many more options. You can use this material in two ways. Choose the one you like best. You can use it as a normal PLA and get prints characterized by a very good adhesion between the layers and high precision. You can also make your prints acquire similar properties to that of ABS – better impact resistance and high temperature resistance. All you need is an oven. Yes, an oven! By annealing our HD PLA in an oven, in accordance with the manual, you will avoid all the inconveniences of printing with ABS, such as unpleasant odour or hazardous fumes. But these are not all the advantages of HD PLA. For the production of this material we have chosen raw materials that are approved for food contact in compliance with the EU directive and FDA regulations. HD PLA is also certified by RoHS.


So, it looks like HDPLA is not the shorthand of a polymer molecule, but rather a trade word indicating that the base PLA has been mixed with additives.  Furthermore, the answer I got via mail seems to indicate that "HD" refers to the high Heat Deflection temperature of the filament (the heat deflection temperature is the temperature at which a polymer or plastic sample deforms under a specified load).