The definition of a dice game is that it requires just dice to play. To expand on that, I would say that a game that requires you to roll two dice to move around a board does not qualify. Oh no, to fit into this category, the game must revolve around rolling dice. It might still involve a board but the key part of play is resolved with dice.
The boundaries are now frequently merging so some games may appear in more than one category. Generally though, a game will go into the category which most represents it and its components. Other subdivisions will occur such as Word Games, but you will discover these as you browse this website. Hopefully it will all start to make sense!