The Wii U Pro does not have any motion sensor so you can't flick/shake/tilt/whatever it to do tricks and such (strictly speaking of Mario Kart)
However, you still can do all of that by pressing some buttons.
Wii U Pro is a traditional controller but it's still capable of doing pretty much everything the gamepad does (minus the screen of course)
If anything, the Wii U Pro was made with a different demographic in mind aka dudes who hate motion stuff, so yeah..
Ah didn't realize that you could do tricks while jumping by pressing R/ZR! Nice