Based on how the NHL calls Rule 69 Interference on a Goalkeeper and Rule 61 Slashing, I am not surprised at all that the referees allowed the Andrew Shaw power play goal to stand. You might be confused as to why I referenced Slashing as well. This particular play illustrates an aspect that is very frustrating to me as a goalie and one to which I have never really seen addressed. But first, let's look at Rule 69. I'll omit less pertinent sentences to keep it shorter.
Under Rule 69.1 - "Goals should be disallowed only if: (1)....(2) an attacking player initiates intentional or deliberate contact with a goalkeeper, inside or outside of his goal crease. Incidental contact with a goalkeeper will be permitted, and resulting goals allowed, when such contact is initiated outside of the goal crease, provided the attacking player has made a reasonable effort to avoid such contact.
For purposes of this rule, “contact,… whether incidental or otherwise, shall mean any contact that is made between or among a goalkeeper and attacking player(s), whether by means of a stick or any part of the body."
Further under Rule 69.3 - "If an attacking player initiates contact with a goalkeeper, incidental or otherwise, while the goalkeeper is in his goal crease, and a goal is scored, the goal will be disallowed."
Shaw plays the puck off of the shaft of his stick and then swings wildly at it, missing it completely and striking Elliott with his stick. See his stick about to hit Elliott in this photo 
This contact would seem to fall under Rule 69.3 and Rule 69.1. Having said that, this type of contact happens all the time and I have yet to see these rules enforced unless perhaps the goalie is hit in the head. As a goalie who has taken countless slashes to the mask, the ribs and the back of the hand from forwards who are wildly swinging and missing pucks or making contact after I have it covered, this has always been maddening.
The other part that is maddening to me is that the Slashing rule almost seems to conflict Rule 69 and give players free reign to swing wildly at the puck no matter how many times they hit the goalie. Under rule 61 - "Slashing is the act of a player swinging his stick at an opponent, whether contact is made or not. .... Any forceful or powerful chop with the stick on an opponent’s body, the opponent’s stick, or on or near the opponent’s hands that, in the judgment of the Referee, is not an attempt to play the puck, shall be penalized as slashing." The last sentence could theoretically provide unlimited whacks of the goalie.
The second issue regarding the Shaw review that I have not seen addressed are comments made by referee O'Rourke that sure seem to suggest the technology the referees are using isn't good enough. According to NHL.com, O'Rourke said that "the contact [with Elliott] is after the puck goes in". This statement is false as can be seen in this photo
The puck is just about to come off his stick as he is making contact with Elliott. Of course, this photo also shows why that contact would be allowable as Shattenkirk is pushing Shaw but the fact that O'Rourke couldn't tell that contact was made before the puck went in should be concerning to all.
Even with the issues, it's still a great day for hockey.