Is there a wii u game that teaches basic martial art or self defense?

Not outside of "rhythm" games, no. Besides, the Wii U has released its last game, "The Legend of Zelda: Breath of the Wild" today actually, and the system will no longer be supported in lieu of the new console, the Switch.

Using peripherals such as the Wii-motes or camera technology for other systems will only get one so far anyway - as others have mentioned, nothing can replace a real, tangible teacher/coach/instructor. Moving around in one's house with no resistance, no one to correct form, nothing to strike against, nobody with whom to spar, etc. is very limiting.

No.

You need an instructor to learn properly. Videos and books can not correct or guide you.
And if you learn the basics wrong it can take twice as long to correct those mistakes.
So the answer is no

No

Unfortunately, martial arts is physical and has to be trained physically and with a partner. Can't sit in a chair and learn something physical. You got to do it and it's not just martial arts, it's anything physical.

My knowledge of wii u is limited, but I'm assuming it just uses the hand controllers like the original wii?
There's a lot of stances and foot work not to mention hand posture in martial arts. There are more problems, but those alone are enough that I'd say no.

youtube would work better.