Mission cards turn Sonic Adventure DX: Director's Cut into an enhanced port of the Dreamcast adventure, not a new numbered sequel. The 2003 cube edition adds Game Gear games and a stack of missions on top of Station Square, the Mystic Ruins, and the Egg Carrier.
Metal Sonic can be met again through those mission goals, and the Chao garden still raises the little creatures hatched from the original gardens. The point of the disc is the first adventure plus those extra tasks, not a numbered sequel.
Players who already finished the Dreamcast story come back for the mission list and the handheld games tucked in the menu. The plot of Chaos and Perfect Chaos stays the one they already know.