How does one actually use luck?
In game theory a lot of real world data is discarded in favor of simplifying the problem we are trying to model (and usually it is assumed both players play to the best of their abilities). A lot of things that affect both players are ignored, because they are not easy to model,. Such things such asare: concentration, familiarity with positions, preferences, skill with each piece, memory, time, etc.
Another important point is that player skill is not something static, ratings should always be considered estimates of true skill, which is pretty difficult to measure since it can vary from game to game and even during a game. But it can be said that highly skilled players commit fewer mistakes than less skilled players.
In other words, it can be said that we are hoping our opponents commit mistakes we can identify and exploit in all games, so in this sense, all players could be said to be always trying to or using their luck all the time and the fact that a player committed one or more bad moves doesn't change that. To notice a mistake committed by an opponent is another one of those skills that are difficult to measure, so is the skill to punish a mistake.
Luck as randomness
White could have lost the game, it also could have ended in a draw. There was no guarantee that 'luck' or randomness would be 'in favor' of any player. So just as white gambled and won, it could have been a loss instead.
In this sense, no player can actually use luck, because it is not a component a player has any control over as both players are subject to randomness.
The place of sportsmanship
That being said, what role does sportsmanship play? In my opinion sportsmanship plays the role of respect/politeness. During a game, if both players agree the game is over and its result, wouldn't it be better to just start a new one? It's another thing entirely if there is no agreement. And the reason for both players not agreeing doesn't matter, though agreeing on the result is just usually faster.