Final Battle - 12

Could you clarify for newbies what "mini-double" means? In our group, do we play 3 games – each player against every other player, resulting in a total of 2 games?

The word "double" refers to "double elimination" (I think that's clear). I don't understand how each player can play against every other player. "Mini" means that the winners of the lower and upper brackets don't play in the grand final but advance to the next stage.
The winner of the upper bracket plays 2 games, while the others play 3.

Another name for this system is "GSL" (let the experts correct me if I'm wrong), but that would only confuse people more. Here's a picture for example: