What the "DS" in Nintendo DS really means

Some say Nintendo DS means "Dual Screen," others say "Developer System," but considering the way Japanese companies love to advertise things in Ingrish, here's a plausible Nintendo of Japan advertisement, focusing on the DS's touch screen and hit title, Nintendogs:

Nintendo DS
Feels so nice
Doggy Style

The whole joke comes from Kotaku, though they say "Dog's Style" instead of "Doggy Style" which makes less sense.