In a true double elimination tournament, half your matches are in the consolation bracket. In this "rechepage" setup, the consolation bracket is basically a tournament of guys who lost to the finalists and everyone else is just out.

Also, eliminating the 3rd place match gets rid of an entire round. In the NCAAs, the 3rd place match is combined with the 5th and 7th place matches. Here, they don't do 5th and 7th, so I guess they also skip 3rd and instead give out two medals.