Clearly the situation you describe has nothing to do with luck. Instead, it is simply bad play by black who cannot turn a decisive advantage into a victory.

The question in the text is actually:

Are you allowed to make strategic use of your opponent's weaknesses? The answer is of course "yes, absolutely!". But framed this way it becomes clear just why it is bad sportsmanship not to resign when one has clearly lost: Because it betrays that you think your opponent is an idiot. Consequently not resigning becomes worse sportsmanship with better opponents. (As an aside, in the game of Go an entirely decided game can be drawn out for a long time if the loser refuses to accept defeat which is therefore much more annoying than in chess.)

An interesting side question is: Is there at all a luck component in chess? It seems obvious that there isn't because chess is a complete information game with no random input. But I'd make the case that there is something resembling luck because while all information is available — after all, the board is right there! — the path of perfectly utilizing that information is not. Chess is not solved. That means that our assessment of positions is imperfect. The superiority of one move over another may only become apparent later. It was always superior, mind you; but we didn't know. This is where luck comes in: We may be lucky and choose a move that later turns out to be great. This kind of luck plays a greater role with weak players whose positional knowledge and analytic capacity is limited. Chances are that a strong player would have recognized the superior move — in fact, this ability is what defines a strong player.

Now to your title question: Can this kind of luck be used as a strategy against a stronger player? That is questionable. It won't work in simple positions with clear paths forward: Those will be understood well by the strong player, hence there will be no bad surprises for them later. This kind of luck therefore can only work in complex positions in which even the strong player's predictive depth is limited. But unfortunately even the limited prediction, the intuition and the experience favor the strong player in complex positions. A weak player will have a hard time conjuring up a lucky turn that the strong player could not prevent in time.

Clearly the situation you describe has nothing to do with luck. Instead, it is simply bad play by black who cannot turn a decisive advantage into a victory.

The question in the text is actually:

Are you allowed to make strategic use of your opponent's weaknesses? The answer is of course "yes, absolutely!". But framed this way it becomes clear just why it is bad sportsmanship not to resign when one has clearly lost: Because it betrays that you think your opponent is an idiot. Consequently not resigning becomes worse sportsmanship with better opponents. (As an aside, in the game of Go an entirely decided game can be drawn out for a long time if the loser refuses to accept defeat which is therefore much more annoying than in chess.)

An interesting side question is: Is there at all a luck component in chess? It seems obvious that there isn't because chess is a complete information game with no random input. But I'd make the case that there is something resembling luck because while all information is available — after all, the board is right there! — the path of perfectly utilizing that information is not. Chess is not solved. That means that our assessment of positions is imperfect. The superiority of one move over another may only become apparent later. It was always superior, mind you; but we didn't know. This is where luck comes in: We may be lucky and choose a move that later turns out to be great. This kind of luck plays a greater role with weak players whose positional knowledge and analytic capacity is limited. Chances are that a strong player would have recognized the superior move — in fact, this ability is what defines a strong player.

Now to your title question: Can this kind of luck be used as a strategy against a stronger player? That is questionable. It won't work in simple positions with clear paths forward: Those will be understood well by the strong player, hence there will be no bad surprises for them later. This kind of luck therefore can only work in complex positions in which even the strong player's predictive depth is limited. But unfortunately even the limited prediction, the intuition and the experience favor the strong player in complex positions. A weak player with an inferior understanding of the complex position will have a hard time conjuring up a lucky turn that the strong player could not prevent in time.