And that's where additive and subtractive design comes in. Through the development of a game, several prototypes are built and tested, to see if the game works, and the games design is altered as a result of this testing, through this you can add or take away from the game to hone in on the experience you want from the game. This is in essence what we are talking about, but to add and remove content from a game doesn't have to be exclusive to during development or testing.
Due to games having greater online connectivity than ever before games can be updated and developers can even create "DLC" aka DownLoadable Content (I don't get it either). While updates are used mostly to patch bugs and correct errors, and DLC is to sell bonus content that often doesn't effect the mechanics or the way the games plays overall and is usually new avatars or levels.
But of course there are some exceptions to these rules, games like Overwatch and MOBA's like League of Legends, are constantly being re-balanced and tweaked in their updates in a constant attempt to keep the game as fair as possible, and not everyone agrees they make the right decisions, so some of these choices they reverse. Warframe and Rainbow 6: Siege are examples of two games that succeeded only because of changes made to the game well after launch.
That does not leave this adaptive design in purely the hands of developers, it can very often manifest in three more ways that are driven entirely by player involvement. Games such as Halo offer many in depth options for customizing and altering game types, objectives, weapons, vehicles and even maps in some of the later games, several fan made gametypes have also been later integrated into the series by the developers making them official gametypes, such as infection a mode where each player has to survive as long as possible and infected players attempt to infect the survivors, where the infected have modified movement and only close range weapons, and Griffball, where two teams have to place the bomb at the other sides post, much like assault, but within a small square arena and only using melee weapons to resemble games similar to rugby or gridiron, the person carrying the bomb also turns yellow to resemble the character from the Rosterteeth webseries
That does not leave this adaptive design in purely the hands of developers, it can very often manifest in three more ways that are driven entirely by player involvement. Games such as Halo offer many in depth options for customizing and altering game types, objectives, weapons, vehicles and even maps in some of the later games, several fan made gametypes have also been later integrated into the series by the developers making them official gametypes, such as infection a mode where each player has to survive as long as possible and infected players attempt to infect the survivors, where the infected have modified movement and only close range weapons, and Griffball, where two teams have to place the bomb at the other sides post, much like assault, but within a small square arena and only using melee weapons to resemble games similar to rugby or gridiron, the person carrying the bomb also turns yellow to resemble the character from the Rosterteeth webseries
made as a Halo machinima, Red vs Blue, Griff.
Another way players can make the later alterations is through modding. Modding refers to players making modifications to a games raw files, whether its assets or code and so on in order to change the experience, for prime examples of this look to any of the recent games developed by Bethesda as they are famous for near limitless mod support. Modding can include stuff as simple as cheating in extra items, to stuff as complicated as your own worlds, stories and possibly even your own game within a game, the potential is endless depending on you ability to make such a thing happen and the support the game offers for those mods.
The final (and most fun) addition (or subtraction) a player can make, are their own homebrew rules. People are most familiar with this idea showing itself as drinking games. Everytime you die, take shot. You must finish your drink before you finish the race, and your kart can not be moving while you drink. Every shot with a power weapon is a shot you must take at the end of the match, every kill you get reduces a shot. This is what I mean by homebrew rules, they don't have to be alcohol related, it's just making up rules on the spot, to make the game more interesting or leveling the playing feel to give weaker players an advantage.
You can add and take away from a game at any point and generally it is a good idea to do so, just don't forget what the core of the game is. Keep it balanced and keep it fair, in the end the player is just gonna screw it up and find a way to get plastered while playing it anyway.