Market share/Units Sold
Won't touch the Wii or PS2. It doesn't have to. At worst, you're looking at Gamecube sales. At worst. However, Nintendo doesn't have that 1 or 2 "WTF design choice" that Gamecube did. Starting with 8GB/32GB internal flash memory was almost one, but having a storage solution at launch helps tremendously. Voice chat is a mess right now though Nintendo can fix that. Wii U should sell much better than Gamecube did, more than N64 for that matter. Despite some growing pains, Wii U is a pretty solid console.
Without knowing what Sony and Microsoft have planned (though I have doubts they'll do anything drastic), it's hard to tell where Nintendo will be in market share. Launching 1st and having at least a year to rack up sales before the competition hits is the difference maker here. That affects everything else. Nintendo can live with getting PS3/360 ports for the time being because it's better than not getting them. By the time Orbis/Durango launch, Nintendo will have sold millions of units. Ignoring that many people (and counting) is leaving money on the table and I don't think 3rd parties will.
3rd party exclusives
There just won't be many of these any more. Nintendo is going to score them in the same way they got Bayonetta 2, picking up projects by talented developers in danger of getting cancelled. Also, Nintendo should treat UbiSoft like their best friend. Nintendo gave them a major boost by making Rayman Legends the ONLY pre-launch store demo. Imagine ZombiU becoming a series and remaining exclusive. A sequel with Ubisoft Montpellier already familiar with the hardware could be huge. Additionally, if Sony and Microsoft don't follow Nintendo's lead in supporting indie developers, they'll likely get tons of eshop exclusives.
Perception among gamers
Considering the GamePad is just a traditional controller with motion dodads and a large screen, Wii U already has more gamer cred than the Wii. Nintendo may want to experiment with Zelda, but it would benefit the Wii U greatly to get it out soon and build on the potential of that E3 demo. The art may not be as inventive as Skyward Sword, but damn, it was pretty. That could be the core game that convinces hold-outs that Nintendo themselves are serious about them.
Graphical capabilities years down the line
I have my doubts that Sony or Microsoft will take on major losses on hardware. They will undoubtedly launch more powerful hardware, but Wii U won't be left too far behind. It has a modern feature set and should keep up with the competition for a few years due to scalability. Wii U will be getting 720P more often than 1080P. The important thing is that they'll still be getting most games for most of its life. I really don't think Nintendo is going to try to push Wii U past 5 years. The last big Wii U games from Nintendo and 3rd parties will likely be released in November 2016, maybe the 1st half of 2017. It's all about timing. Nintendo stuck with the Wii longer than they should have. Wii U is an HD console amidst other HD consoles. It should hold up better than the Wii.