They can, and hopefully they will..

I guess it depends on what people define as relevant. If selling 4 - 10M copies of Mario Kart, Smash Bros, Zelda, and Mario on a userbase of 10 - 20M devices is relevant then yes. If you expect them to compete with Sony, Microsoft, Apple, and Google, then I would say no chance in hell. Even Sony is on the cusp of falling to the other 3, unless they can make a mobile PlayStation brand that can compete with iOS, Android, and Windows 10.

As far as I see it, Nintendo will never be the market leader in gaming in the future.

This only applies if the Handheld portion has cellular services and an unlimiited 4G connection. People are not going to by a second mobile device, so it has to be able to replace thier current phone. This is where Nintendo and Sony screwed up with 3DS and Vita. If the 3DS had 3G and cellular service from launch it would have a userbase over 200M right now. Handhelds are not on a decline because people don't like the from factor, or a versitile mobile platform, they are suffering because there is very little room left for a non connected device in todays world.

I feel like you wanted to ask "WILL they make a relevant console again?", not "CAN they make a relevant console again".

They CAN, I'm not sure if they WILL.

Well Wii U is only 3 milion unit sold behind X1, they are kinda competing *escapes from the building jumping out of a window*

I wouldn't call any Nintendo console "irrelevant" - except the Virtual Boy. Just not as relevant as they should be.

That's a non-starter, people use their phones for a lot more than just making phone calls (hell, that's about the last thing I use my smartphone for). 

The smartphone is the central tech and social hub of people's day to day lives, they're not going to give that up for a silly portable console that has some phone features on the side. No way in hell. 

And if it ain't Android or iOS no one is touching that with a 50 foot pole (ask Microsoft and Blackberry). 

So you're never going to get them to take away their smartphone is their pocket. Where you may be able to make some headway is in the budget tablet market ($250 and less). If you can release a good tablet that also can double as game handheld with physical controls, and you sell it at cost (thus undercutting every other tablet), relying on games to make money on ... yeah I could see that doing OK. 

I think Apple overcharging for the iPad has kinda stymied their momentum in that market ... people don't want to pay $500 for a tablet. 

Last one was relevant home console, I can't see why they can't do it again.

Well we should compare the X1 numbers of 2016 with Wii U's 2015 numbers for that, since the U launched a year earlier and for as far as I know the X1 kicked the Wii U's ass this entire year. And the console is competing with the PS4 where the Wii U really isn't with it's 3.5 million units a year.

Unbelievable, what kind of mental trap do the current mobile market leaders have on people to make them think this way. It is absolutly insane to think that no one can ever touch the mobile space ever again. 

Where does the idea that a piece of glass with such limited functionality is a serious piece of tech, and a device with pysical controls is just "a silly portable console" come from? Are people seriosuly in so much of a fog that they can not see the major limitations of the current mobile leaders? 

There is absolutly no reason Nintendo can not make an OS that is just as capable of integrating Social Media, Diet & Health Trackers, E-readers, Mobile Banking, Productivity Applications, Video/Audio/Photo Editing, and much more, while still maintaning a gaming centered enviornment at the core. The same applies for Microsoft and Sony, both comapnies could easily make a gaming centered mobile device on their own OS that matches or outshines the current leaders in every aspect. 

Blckberry and Windows Phone are struggling for a multitude of reasons, but the biggest one is they are trying to beat the current leaders by doing the exact same thing. The only way to ever compete or have a shot at claiming a position among the leaders, is to come at this with a different approach. One which brings something new to the market, while also being just as good or better than the current leaders at what they already offer. 

Nintendo is not incapable of bring out a highly functional Portable Console which has more functionality than what is offered on phones today. The device can still be a gameing centric device, but with the versatility to be much more if one desires to use it in a different matter. If done right, someone with no interest in games could buy it, and get a better experience than their current phone while never even touching the gaming part of the device. If they can do that, and bring the same level of operation to the home platform as well, then they will not only be relevant, they will have a shot at being the leader of home and mobile electronics.