Winger goals are quick release goals that don't require any real puck skill. Like Chiasson's goal yesterday.
Stop trying to make "winger goals" happen. It's not going to happen. It's definitely a type of goal if you want to categorize types of goals, but calling it "winger goals" is misleading, because it implies that the type of goal you score is somehow a result of the position being played.
Realistically, the type of goals you are calling "winger goals" are just the type of goals scored by goal-scorers. Look around at the centres around the league who score a lot of goals. Crosby, Stamkos, McDavid, Seguin..... if you look at all their goals, you're going to see a ton of back-door tap-ins and rebounds. If you want to be the guy who scores goals, you have to be willing to not have the puck on your stick leading up to the goal, because the way defence is played these days in the NHL, you're not going to be able to consistently walk through defences and finish.
And if you're going to say that goals that do require puck skill are "centre goals," why would you make that delineation, given plenty of wingers like Patrick Kane and Jamie Benn (and one Jonathan E. Gaudreau) rack up those types of goals?
As others have said, the position you play on forward doesn't really matter in the grand scheme of things once the play is in the offensive zone. What does matter is the type of player you are and your individual tendencies. I would say position makes a great deal more difference on zone exits and defensive and neutral zone play, and this is where Monahan needs to shape up.
But I don't think he is playing in a way that would be conducive to the wing either. His instincts seem fine, but he's moving really slowly and doesn't have the confidence to take the game to opponents. He looks really tentative, and that's a huge difference between him and Backlund right now, who is playing so much more confidently. Can you see Monahan, the way he is playing right now, being effective on the walls, taking outlet passes and then getting his ass moving up the wing to provide an option? The things he's struggling with right now at centre are going to hold him back regardless what position he's playing, and they're things he's been good at in past seasons, although I realize you disagree with this.