The dividing line is historical lineage: chess-family games descend from or parallel Chaturanga, while modern conquest games like Risk have no such lineage.
Chess-Family War Games covers the chess family proper, games of differentiated armies descended from or parallel to the historical game of Chaturanga, including Chess, Xiangqi, Janggi and Shogi, where each piece has its own rank and movement rule. Modern Conquest and War Games instead covers 20th-century commercial games such as Diplomacy, Risk and Stratego that have no traditional chess-family lineage, so the dividing line is historical lineage rather than theme.