I checked out that link just now. You can delete and redownload on your Wii but once you transfer to the Wii U, you'll only be able to delete and redownload on the Wii U.
Sucks because I can play my Xbox purchases on any 360 as long as I log in and I can play my PS3 purchases on any PS3--sometimes, on a PSP or PS4 or Vita! Nintendo really needs to quit being so restrictive on digital downloads. It makes me not want to buy anything digital. Can't even share my 3DS purchases with my daughter or even get club nintendo points for them.
Do tell me how you can play any PS3 purchases on a PS4, would love to know. I have no option to do this on either the PS4 or the Xbox One. At the very least I am happy I can play my Wii purchases on the Wii U, though again disappointed I can't have them on our SECOND Wii U.
PS1 classics. Or some indie games like Flower*.
*see my sig
Does that not require purchasing the game again though?
Nope. The same PS1 title I purchased for PSP back in 2009 is downloadable for free on my PS3 and PSV. Even the saves can be transferred between consoles (though the process is cumbersome). I bought Flower for PS3 and I was able to download it again for free on PSV and again on PS4!
We only have one Vita but back when my daughter and I were PSP fans, EVERY game I bought digitally, I could play on her PSP and mine with no restrictions. We bought a ton of games, too!
Meanwhile I've purchased 1985's SMB1 on Wii, Wii U (at reduced price), and 3DS. Has to pay every time. Nintendo makes your purchases playable only on the device you purchased it on. I can't even get Club Nintendo coins for the copies of Animal Crossing and Mario Kart 7 I bought digitally for my daughter's 3DS since the last big update. I can only claim digital purchases on one 3DS now even though both are registered as mine.