I see no issue with the goal. When a player breaks his stick and doesn't drop it, the refs more often than not warn the player before they call a penalty. The stick break and goal all happened so quick it is irrelevant really.
You see no issues with the goal?
The refs do not give warnings. If a player plays a puck with a broken stick, and the ref sees it, it is always a penalty. ALWAYS. Even if the player doesn't know the stick is broke. They may yell at the player to drop his stick immediately (because the player might not know it is broke) and if he doesn't drop it right away, it is a penalty...but there is never a warning given.
A player can't even skate around with a broken stick. He has to drop it immediately or it is a penalty.
It doesn't matter if the play happened fast or not, or if he was slashed or not (he wasn't), the correct call is still a no goal and a penalty.