In its first three days on sale, Splatoon 2 sold an estimated 670,955 copies at Japanese retail.
Typically in Japan, new Pokémon games sell well over a million copies in their first few days out. For example, Sun And Moon sold 1,905,107 copies at retail. That's at the extreme end of the spectrum, and generally speaking, successful home console games, however, tend to sell less than that in Japan. While the Switch is both a home console and a portable, it still doesn't have the huge install base to make sales numbers like that possible.
According to Famitsu, Nintendo has sold an estimated 1.2 million Switch units in Japan as of July 23. That means that over half of those Switches seem to have copies of Splatoon 2! Thinking about it that way makes Splatoon 2's sales numbers even more impressive.
Here's some extra context: As Kotaku previously reported, the Switch version of The Legend of Zelda: Breath of the Wild sold 186,379 retail copies in its first three days, making it the biggest selling game that week. (The Wii U version sold another 44,602 copies.) Since Nintendo sold 330,637 Switch consoles in its first week in Japan, that also means that over half of Switch owners picked up Breath of the Wild at launch.