This question is sort of a generic version of How should we tag questions. There is some talk in there about the board-game tag, but it's lost in the noise. For me, these two tags are clearly duplicate tags: boardgame, board-game and board-games. But there are really two things at issue here:
Is there ever a time a tag should refer to a plural entity? For me, no. I think this is a variation on the wiki NamePluralProblem. Wikis tend to use the singular always unless a page is only ever referred to in the plural. But bigown clearly felt differently.
More subjectively, does a site dedicated to board games really need a tag 'board-game'? My vote is no, seems pretty redundant. I also expect, however, that these are the kinds of tags that will show up over and over again and for that reason, we should preemptively just make one so that the site can exert control over it. Beside 'card-games', what other tags might fall into this category?