A PvP duel is defined as a match between 2 players. Said duel follows these steps:
1) The players search for the duel
2) The players enter the duel
2.1) If one player enters the duel and the other player does not, the player who has entered the duel leaves and returns to 1.
3) The players play out the duel
3.1) If a desync error occurs sufficiently early that playing it out against the AI is not useful, return to 1.
3.2) If a desync error occurs when playing it out against the AI is useful, both players play out against the AI.
3.2.1) If both players defeat the AI, return to 1.
3.2.2) If one player defeats the AI and the other does not, the player defeating the AI is awarded the win.
3.3) If a player accidentally or otherwise leaves the duel after it begins, that player is awarded a loss.
4) The winner of the duel wins the duel.
The crux of the issue is thus at what point the internet failed. If the internet failed before the duel began, this falls under 2.1 and the game should be replayed. If it happened during the duel, it falls under 3.3 and the game is a win. These rulings are consistent with the definition of a PvP duel (between 2 players).
Let us examine the first screenshot that Spielkind took:
http://imageshack.us/f/834/bogtro1.gif/a) This is a screenshot of remarkably poor quality. It is not clear whether this is even against me. However, we can assume such since the deck was correct.
b) This is a screenshot that clearly shows the first turn, with Spielkind winning the toss.
c) The timer is about to expire, clearly implying that I was not in the game at the time.
Let us examine the second screenshot that Spielkind took:
http://imageshack.us/a/img210/4899/bogtro11.gifa) This is a screenshot of remarkably poor quality. It is not clear whether this is even against me. However, we can assume such since the deck was correct.
b) This screenshot shows the turn before Spielkind won.
c) You can see there is no longer a timer, implying that AI took over.
So the course of events was clear. Spielkind entered the game, watched my time run out, and the AI took over. This is the definition of not being in the game.
Therefore, I was not in the game when my internet failed. This is agreed upon by Helston in very clear terms, and quite probably by Spielkind as well. How this is an unclear situation is beyond me if ALL evidence points to me not being in and everyone agrees that I was not in (even non-interested third parties have commented on this). However, the ruling was apparently based on a quote by RavingRabbid:
"NEIGHBORS... no"
"This is either a 0 pend draw or..."
"a 0 pend draw"
This apparently implied to the WMs that awarding a win was in order.
This is not the first time this situation has occurred. It has occurred on at least two previous occasions in War, both of which were ruled replays. It has additionally apparently occurred several times in non-War PvP, with the ruling again being replays. With this ruling, far from removing ambiguity, we have confused the issue for all future times this situation occurs. There is now precedent for both a replay and awarding a win (though, fortunately, more for a replay)
How the ruling was achieved is also slightly disappointing (and already addressed by Helston). The ruling was made without any sort of screenshot proof whatsoever (these screenshots were sent after the ruling was made), and the WMs did not apparently seek input from either player (they possibly may have spoken to Spielkind, but the implication is that they did not). The screenshots that were eventually provided were of poor quality and barely readable. They hardly even count. Effectively, the WMs ruling was based on no evidence, no real account of what had happened, and no investigation of precedent. It would have been more fair to flip a coin.