That seems like a rather uncommon variation upon the double elimination concept, as it departs from the commonly understood notion that a player is eliminated if and only if they lose two games.
As a design choice, this current implementation might have some benefits, such as making the length of the tournament slightly shorter and more predictable. However, I think that this comes with the drawback of introducing some unfairness.
One of the motivating factors for using a double elimination format (as opposed to single elimination) is that players have the safety net of the bottom bracket to avoid immediate elimination from having just one bad game. This design choice basically takes away that safety net for the player that hasn’t used it yet, once the tournament has been reduced to two players.
Also, a fairly common occurrence in double elimination tournaments is that the final two players have already played each other once before. In that case, one can think of the final one or two games in a typical double elimination tournament as finishing the best-of-three, head-to-head series between these final two players.
On the other hand, reducing the final match-up to just a single game (as is currently done) can result in a somewhat arbitrary determination of the winner. If the player that had previously lost wins the final game, you wind up with a symmetric situation between the top two players, where both have won all but one game, and they have split their two head-to-head games, however, the player that lost first gets awarded the win. This was the case in the Thyderion’s tournament and the second other example that I gave above.