In a way, Argo is both correct and incorrect. Since he apparently is defining luck as far back as the situation you were born in and your genetics, then in a way, he's correct. All things being equal, the person born with the more compatible skill set for a certain game will usually end up victorious. A person born with genetics that will make them 7' tall will likely beat someone born with genetics that make them 5' tall in a game of basketball.
That being said, all things are NOT equal. Unless we exist in a vacuum (which we don't), what you are born with is not the final picture. Let us again take my example of a 7' tall player and his 5' tall opponent. For simplicity's sake, let's assume they are twins so that they have the same socio-economic opportunities. Now, on the surface of it, the 7' tall player has the genetic advantage. However, let us assume the 5' tall player practices extremely hard and becomes a master at shooting 3 pointers and learns how to maneuver around his brother while the 7' tall player coasts by on his natural luck to be born tall. If the 5' tall player begins to beat the 7' tall player, would it still be luck? No. It would be dedication, hardwork, and skill.
The same goes for Diplomacy. The person who works hard at analyzing tactical positions and possibilities and investigates his opponents to learn their strengths and weaknesses will likely end up the victor, whether or not he was "naturally lucky" to be born with the right skill set. Why is this? Because unlike Argo's assertation that "rational" players must be "random" when multiple "rational" paths to victory exist, that simply is NOT true. Pretty much every player has a tendency that can be exploited. Many players are cautious and play to prevent a worst-case scenario. Others will strike out boldly in an attempt to get that big breakthrough. The "skill" part of Diplomacy is learning your opponents and using that knowledge against them. If I know Devonian is usually aggressive, I can plan my tactics around that.
Will I sometimes be wrong? Of course. No strategy is foolproof. That said, it is not luck that made me wrong. If it was pure luck, then I'd have a 50-50 shot of being right when there are two options. Using your skill and knowing your opponent, you can swing that chance in your favor and have a better shot at ending up victorious. Otherwise, if it were "luck", then there wouldn't be a large disparity amongst top players. We would see every rational player rated approximately the same since the same "luck" effects all of them. As we do NOT see that, we can thereby deduce that it is not "luck" that is the definitive factor.