This post is from a long time ago but I decided to put in my two cents (also, forgive me if my grammar and referencing is poor. I'm writing this on my phone. The constant scrolling up and down makes me not... Work at my optimal levels)
I am going to go watch a game. (Intention: go watch a game)
I am going to a game. (Just going to a game. Most likely to watch, because what else are you going to do at the game. If you're not watching, you would use other words like play or work or something else. And you wouldn't say "a game", you might use "the game" for any other intention. These would need more context)
Intuitively, if I heard either, I would assume you have an intention to watch a game. If you were to be playing in the game, you would most likely use "play" instead of go. So there is absolutely no difference.
With respect to golfing... That one is special considering that "golf" can be used as a verb meaning "play golf" and with that being said, golfing would then be a noun for playing golf as running is to run. Unlike other sports, except in slang (I'm gonna go ball, Mom. Don't wait for me), we don't use their names to refer to playing the sport. So...
I am going (to go) golfing when my wife gets home.
I am going to golf when my wife gets home.
I had to modify the sentences a little here to get a better feel for how the words might be used. As said previously by another commenter, they need more context. Alone, they sound pretty similar.
Here, the first example sounds like you intend to go play a game of golf once your wife arrives. In the second, it sounds more like you're going to do it in the house (possibly just to annoy her or something). Also, in the first sentence, you could take out the "to go". It would function in the same way as "I'm going home tonight". The sentence construction "I'm going noun" seems to work fine for certain places and activities but then not others. I can't put my finger on why... I would love input on this.
I'm going home. (Sounds fine)
I'm going bowling. (Sounds fine)
I'm going running. (Sounds fine)
I'm going golfing. (Sounds fine)
I'm going school = awkward
I'm going eating = awkward
I'm going writing = awkward
Similarly for activities that can be done in many different places, let's use "watch a movie".
I am going to go watch a movie. (Implies I need to go out, or away, to watch the movie. This usually occurs at the movie theaters/theatre, cinema, whatever the hell your dialect of English is).
I am going to watch a movie. (Ambiguous. I may be going out to watch it, or I might just be doing it at home).
Now let's get to the Canada one.
I'm going to go to Canada. (This is a noun/place. Not a verb. I intend to go to Canada)
I'm going to Canada. (Same thing. Doesn't change anything except you've shortened your mode of expressing your intention).
Context
Q: What are you doing this summer?
A: I'm going to go to Canada.
Q: Where are you going this summer?
A: I'm going to Canada. (I'm going to go to Canada is fine, too)
Q: What are you doing this summer?
A: I'm going to go play golf.
Q: Where are you going this summer?
A: Nowhere. I'm staying at home most of the time. When I'm not at home though, I'm going to play some golf. (In this case, ambiguous. Activities like golf you usually do outdoors, I don't know if you're home has a golf course or not. You can mean play golf in your backyard or go out to play. I don't know.)
So, I guess, all in all, for the sometimes ambiguous activities, I would say if you were "going to go do something", I would assume you had to leave to go do it. Otherwise "going to do something", it could be done anywhere.
One more thought. You never ever say "I am going to shopping." Hell, you never ever say "go to shopping". In the two seconds I've spent thinking about this, I can't think of when you would say this. Likewise, I would never say "go to golfing". We usually say "go shopping" or "go golfing".
I am going shopping.
I am going to go shopping.
I am going to shop (needs more context. Sounds more like something you would say as an exclamation once you got to the mall/store/shops)
Actually... One final thought. Really. This is totally tl;dr. English has so many verbs and ways of saying things that I have to say, what might not sound normal now may sound normal in the future just by the process of people using it so much. To reduce ambiguity or uncertainty or if we accidentally screw up the way we say things by, say, forgetting to use the proper aspect, we usually "fix" it by adding other words to make it clearer. For example, my friend is late when I asked him to be here at 8 sharp.
Me: Why are you late? I told you to come at 7:30.
Friend: I was going, but one of my wheels fell off. (Not the greatest of grammar but I can infer that he was in the process of going (or coming depending on your point of view), but wheel had fallen off causing him to be late. The wheels falling off could have happened before he even jumped in his car or while he was driving. If he'd said "I was on my way but one of my wheels fell off," that would be a different story)
Now, considering I haven't taken an English class, especially a grammar one, in I don't know how many years, if you understood what I meant, then I feel like I have succeeded.