Te DS was not traditional at all, and its success is completely separate from the Game Boy. In fact, when Nintendo released it, they constantly referred to the DS as their "3rd pillar" to distinguish it as separate from their Game Boy line and console line. They had no idea it was going to be this successful. They even released another Game Boy after the DS to appease us oldschool Game Boy fans.
More girls and elderly play the DS. And yes it changed game design. The DS is the reason there are dozens of Nintendogs clones and Brain Training clones on every system. And the DS opened the floodgates for really cheap really quick pick-up-and play games of every type, from Cooking Mama to Trauma Center to Touching the Dead.
And the image of the industry has definitely changed. Now video games are played live at the Oscars, and on Oprah, and on Ellen, and on Colbert, and on Jimmy Fallon, and on cruise ships, and in convalescent homes, and in physical rehabilitation clinics. Those are all the Wii. You think that would've happened with the SNES or PS1? During the SNES years Congress was considering regulating games, and to this day many states are constantly introducing bills to make it illegal to sell M-rated games. The Wii is the family-friendly force changing all that. The DS to a lesser extent, because a whole family can't play a DS at the same time.