Identification of unique DIY floating shelf bracket
They're called "custom-made brackets, specifically for this product". Otherwise known as "bespoke".  

You should be able to buy one of these from the company, dismantle it, and send a specimen to a metal fabrication shop, who will make as many as you please for you. Of course, by doing so you'd be violating their patents or design rights.  If you can find a "maker space", they also have the light metalworking tools needed to replicate such things, and you can rent time on their machines, often by a monthly fee a-la a gym membership. 

You would be better off designing this differently anyway. Not least, since it's holding books, it ought to go into studs or bricks, not hang on drywall (which is basically chalk and paper). As such, the supports will need to be physically on top of the studs, which means you need to be able to move them back and forth. 

You could use plain old L-brackets for the top anchor, with the L angle folded down against the wall so the books hide it.  For the bottom anchor, you don't actually need an anchor; simply screw into the bottom rail a bumper of the right length, and let that hold it at the right distance from the wall.  You could also use L-brackets as in above.