Cheating is breaking rules that you agreed to
I'm an avid board / card / tabletop gamer, and I also enjoy video games. I like to play a wide range of games, including strategy, deduction, dexterity, party, puzzle, adventure, etc. In some games, particularly games that have some sort of moderator (human or computer), there is little to no opportunity to play in a way that isn't consistent with the rules of the game. Even if you don't know the rules, the moderator won't let you accidentally break them, let alone intentionally. However, in the general case, taking actions that are against the letter and/or spirit of the rules is a relatively straightforward proposition. Doing it without getting caught might be a challenge, but it also might not, at least temporarily.
Sometimes, some or all of the rules of a game are written down right next to the game, so all the players can see them while playing. Casinos print some of the rules for a game right on the table where the game is played. Plenty of tabletop games include reference cards that summarize the most important rules like the order of actions in a turn or round, the valid actions to take, costs for those actions, etc. Almost all professionally published games include a rule book that describes 80-99% of the rules of the game, and hopefully at least some of the players at a given table have read the rule book for the game being played. Some games even require players to explicitly acknowledge the rule set of the game at the start.
Games also have unwritten rules. Some games only have unwritten rules, because they have never been published in any consistent fashion. Many games have rules that are passed down verbally, including ancient tabletop games, playground sports, etc. These rules tend to develop over years and decades as the game is passed from person to person through explanations. They can diverge over time and in different places, so “one game” with one name could be wildly different when played with different people.
Most games without centuries of history have edge cases that haven't been contemplated before and so no rule has even been spoken, let alone written. Players discover these edge cases while playing the game. Perhaps they engineer a totally novel scenario that the rules don't sufficiently cover. Perhaps they are planning a strategy that relies on some ambiguity in the known rules. These cases might require adjudication by an authority, a discussion among the players, and perhaps a compromise.
Most confusingly, sometimes two players will each have a reasonable expectation that they are playing a game with known rules, but the games and rules in question will be different from each other. Perhaps there are two games played with all the same pieces, like Checkers and Draughts. Perhaps there are two popular rule sets for a game, such as the different official published rules for scoring small cities in Carcassonne. Both players think the other player has agreed to play by some specific rules, but they are both wrong.
Sometimes, agreement to a rule can be implicit. If a game has just one set of officially published rules, it is usually reasonable to expect that players are implicitly agreeing to those rules if a game starts without other discussion. Sometimes the agreement is explicit, when players discuss and choose a rule set or house rules at the start of a game.
However, sometimes there is no agreement. Players might discover in the middle of a game that they have been playing by different rules. In that case, no one has done anything wrong. The players should have a discussion and decide if they want to continue playing after ironing out the misunderstanding, or if they want to stop playing.
And, of course, sometimes players intentionally violate the rules, doing things they agreed not to do, taking advantage of the other player. When this happens, the best course of action is usually not just to stop that specific game, but to not game with that person again unless something changes and there is some confidence that the rules moving forward are understood and agreed to and will be followed.
This post is about romantic and intimate relationships. Try reading it again if you didn't realize that the first time through. My goal here is to help people who have trouble with “is this cheating?” or “what should I do when I catch them cheating?” in a relationship but no problem with the same question in a board game. I want them to realize that it's the same question with the same answers in analogous scenarios.
PS: In discussing this post in advance, my favorite parallel is “Person who goes online to complain that a game has been unfulfilling and upsetting repeatedly and they don't want to play again, just to be told by many more experienced people that they [were playing with people who] had failed to read or understand or follow the rules, and that things would almost certainly go much better if they resolved that underlying issue.”