There was a lot of daylight between those two Oilers at the time the shot was taken. Skinner is 100% snoozing on that play not expecting the shot and you can see it by how slow he gets into the butterfly. The puck is already coming out of the net when he actually gets into his butterfly. Thats a goalie saving face that he "didn't see it" when he really was just snoozing and not expecting the shot. Reading your response perhaps we agree on that point, he's not dialled in.
It had some impact on the game. The first goal was largely on Foegele and Bouchard and a bit on Skinner on not giving the team a quality save. The second was a bad bounce and a very nice finish by Kempe no fault of anyones really, and the 3rd that they allowed was a defensive mix up, which again Skinner should have stopped due to Nuge's back check, but we can largely blame the D on that one. No, they didn't have a great game as a line, and Foegele especially was bad, but the game as a whole was significantly tilted in Edmonton's favour.