While not a fantastic system, WiiU is more relevant than XboxOne imo. The question is : can they keep up with Sony and MS and win back the core gamers at large? Very difficult to answer atm. Depends on whether the 3rd parties are on board again, some like SquareEnix, Bamco and KT seem definitely too busy making PS4 games to allocate time and resources to NX. Capcom seems to side with Sony on the home departement and western publishers deeply distrust Nintendo. Also, NX needs to be as powerful as PS4, with a solid online & social infrastructure and I'm not sure Nintendo is willing to take the cost of that.

nintendo currently doesnt care about relevance in the market as much as they care about being "different". they are completely out of touch with the market and the WiiU shows exactly that. without a serious shake up in the companies culture and future direction i doubt they can be relevant again in the console market. though this is Nintendo after all, so saying it certainly wont ever happen would be foolish. however, with how things are going, i just dont see it.

Whats the point of debating with you if you truly believe the only new idea Ninty can come up with is another Wii remote? Ill leave the new experiences to Ninty lol not some nobody on the internet. Ninty will never pull a new Wii/DS? We're talking about a corporation that will probably be around for a very long time.

Most likely, no.

There is the off chance that Nintendo releases a cross market device that extends outside of their core market, but the company's success hardly hinges upon unexpected bullseyes like the Wii.

They haven't been competing directly with MS or SCE since the GC and the notion that Nintendo can release another console that will go head to head with a directly competing product as the main console platform of a generation is a borderline fantasy at best.

But if the question is whether Nintendo can release a console that won't win over the core console market but will create another expanded market, one would be counting on the company releasing a product that is of minimal to greatly reduced interest to the core gaming market. Is that what Nintendo supporters really want from the company?

But if by relevance, one means will Nintendo release a console that will continue to generate profits for the company, thus insuring its continued existence as a platform for its own franchises/IPs, then yes; absolutely.

Of course they CAN...however that doesn't mean it WILL...and most likely WON'T...

If we look at the last two Nintendo console's that had any real marketplace success we find the Wii and N64 (particularily in North America early on sold huge numbers). 

But if look at what caused the success of those two consoles, we find breakout hits bringing in a wider audience than Nintendo would have otherwise:

GoldenEye brought in lots of non-Mario fans and kept the system afloat for pretty much like a year until Nintendo could get Zelda:OoT finished. 

On Wii ...

Wii Sports was actually largely driven by college age-adult age gamers. 

Both games are successfully in part because they are not so overly cartoony/over-mascot-ized to turn off adults. Wii Sports would not have the same appeal if it was "Mario Sports" instead. 

And GoldenEye would not have the same appeal if it was "Mario Paintball Shooter" either. 

Games like Bayonetta, Devil's Third, Xenoblade, are too hardcore/niche and don't invoke what people really like about Nintendo games (easy to pick up and play, multiplayer oriented), but people don't want mascots in every game and this is a problem for Nintendo. So they are not the answer either. Even Nintendo Land got this wrong ... went too cartoony/child-like in presentation. 

Mario is like a nice colonge, it's fine to use it, but if you douse yourself in a colonge, even one that smells nice, it's going to be a turn off to people. 

Nintendo needs to find new IP that connect/resonate with adult/teenage gamers in the way GoldenEye and Wii Sports did (two very different games). Until they do that, they will be stuck selling to basically the same crowd of "Nintendo Lifers", which is only 10-15 million strong and a small portion of the kids market (kids like any type of video game, so Playstation or XBox is just as appealling to them as Nintendo is). If that's your audience, you simply will not have a successful home console. 

Yes, if they choose me as CEO.

There's a Nintendo Dreamcast here: http://www.ingsoc.org/

They have the cash, so they sure can.

There is always a chance. I'm sure they know what they will have to do. Now if you are meaning outselling the Playstation of that gen, well that might be a different story, but again, it's hard to say. If the NX is indeed a hybrid/fusion or whatever you want to call it system, they have a very good chance. Nintendo has never been irrelevant, but some consoles have certainly been over looked. They will need better backing from thirds and have a comparable system tech wise because that seems to be what consumers want, among other things. If many of the rumors and such are true, it actually looks like they are heading that way.
Every Zelda game is relevant, as is every game with Mario and Pokemon. How relevant can be argued, but every time these come out they are always compared to the widest array of games and tend to be very high quality so they get noticed. Even if they are on a system that is being over looked it brings that system up a notch in being noteworthy.