Ben Hollerbach,
Correct, in most senses but you're also interchanging sport and game and they are very different for the purposes of what I am discussing, especially as it pertains to the rules.
The SPORT of golf is to simply maneuver a golf ball from Point A to B. You do this by playing a stroke and that is the ONLY way by which you may advance the golf ball.
Every layer from here on out adds a game element to it. Want to compare how you do that over the course of a several holes? That's Stroke Play. Want to compare each hole with another fellow player and see who can win the most holes? That's Match Play. Want to cap the scoring at 6 and then assign weighted points based on performance from hole to hole? Bingo, you got Stableford!
The stymie is definitely in the realm of the game aspect. In fact, it flies in the face of the sport aspect because an opponent's golf ball is NOT an integral part of the course. There is nothing in the SPORT of golf that says part of your maneuvering should consider an opponent.
Playing alone is more a measure of ability than it is a game since, even in economics, a game requires an opponent.
SPORT is *never* fair. Hunters don't cry that's it's unfair if their quarry moves in an unanticipated manner. The kayaker doesn't complain that the river is "unfair." They just go do it and if a course is beyond their abilities they move up a set of te... rather... they find an easier class of rapids.
Games, if they are to be interesting, are almost always regulated to be *more* fair. Take an athletic game such as American Gridiron Football, for instance. If it were a true sport, the fields of play would vary greatly. Out of bounds may be non-existant. Players could use whatever means necessary to impede their opponent, etc. But if this were the case the team that built a lead would simply give the ball to a marathon runner and it'd be game over. So we add boundaries, make arbitrary rules as to why and why not you may impede the other team in certain ways, etc. All to be more fair and to make the athletic challenges more interesting and balanced.
Baseball, too.... there are more rules governing what a pitcher may and may not do (so as to not give the pitcher an unfair advantage) than there are in the entire rule book of golf! And that is before ANY action happens on the baseball diamond. The Infield Fly Rule is one of the most game-y rules and it is there to make something MORE fair.
Golf also differs in the sense that, in order to proceed, a player MUST play a shot. Why must the player farthest from the hole play first in competition? That's completely arbitrary and works just as well the other way around.... that's a rule of the GAME but it does not effect the SPORT.
To take your playing alone comparison into proper context... when you go hiking, or kayaking, or other things for SPORT, do you have a goal in mind? Are you hiking for time? Duration? Or are you there, as the adage goes, because it's there?
Furthermore, it is only possible to win a hole in match play by not holing out in fewer strokes than your opponent when your opponent does something procedure-wise to disqualify them from the hole - which coincidentally - is a GAME rule.