While Youtube launched an app for the Wii U, it has proven vastly inferior to using youtube through the Wii U browser, as the app has no touch controls and a terrible navigation system. So I was horrified when I recently discovered that youtube videos would no longer play in the browser.
Fortunately, someone on reddit has suggested a workaround. Go to the video you want to watch. At the top of the browser is the location bar. Tap on that and replace watch?v= with embed/. For example, youtube.com/watch?v=Cpc-t-l would become youtube.com/embed/Cpc-t-l. Then it will play just fine.
Why did Youtube make this necessary? Was the change made specifically to force people to use their inexcusably bad app? If so, suck it, Youtube.