This puzzle is part of the Monthly Topic Challenge #7: Board games.
Instructions (adapted from The GCHQ Puzzle Book (2016) and the introductory puzzle here on Puzzling Stack Exchange): The words in the following list can be partitioned into equal-sized sets depending on words associated with them; each set has its own word association method. This list is arranged so that these associated words are in alphabetical order. One of these sets is missing a member, so you have to work out where in the list the associated word fits alphabetically, and hence where the word itself should appear in the list. The list should be read from left to right and top to bottom and is only written in columns for convenience. (See the introductory puzzle for a more detailed explanation and an example.)
The question to answer is:
Where does 'NUMBER' fit in the following list?
Crucially this time, every set relates to board games in some way.
In the first instance, please hold off posting partial answers unless you think you have found at least half of the correct word associations (although if you make it that far, why not push to complete the whole puzzle!). Thank you, and enjoy!