The AHL rules are a little different from the NHL on this (I thought they were the same):
http://cdn.rapidmanager.com/ahl/files/11_12_AHLRuleBook.pdf
83.4 Disallowed Goal ? If the puck is shot on goal during a delayed offside, the play shall be allowed to continue under the normal clearing the-zone rules. Should the puck, as a result of this shot, enter the defending team?s goal, either directly or off the goalkeeper, a player or an official on the ice, the goal shall be disallowed as the original shot was off-side. The fact that the attacking team may have cleared the zone prior to the puck entering the goal has no bearing on this ruling. The face-off will be conducted at the face-off spot in the zone closest to the point of origin of the shot that gives the offending team the least amount of territorial advantage.
The only way an attacking team can score a goal on a delayed offside situation is if the defending team shoots or puts the puck into their own net without action or contact by the offending team.
The AHL rule is clearer in this situation because it deals with clearing the zone. The video clearly shows it was a delayed offside - an opposing player was in the offensive zone when the shoot in entered the offensive zone. Therefore, clearly under the AHL rules, the goal should not have counted.
So the Marlies didn't just get a crazy, unlucky bounce - without question, they got a bad call to go with it to cost them the game.