Keep catering to the core, by try to get more 3rd parties on board again.

Not at all. If Nintendo had released a Hardware on par with PS/Xbox and secured the same ammount of third party support(Different from GameCube era), I would not own a Xbox One/Wii U combo right now, since it would be by no means necessary.

The problem of Nintendo this gen wasn't Third Party support, It was the hardware. No one would buy a Wii U with the more Powerful PS4/Xbox one around the corner.

Focus on your core fanbase and kids, don't ever sell the console at a loss, make your games and continue doing that until that isn't financially viable anymore.

Or *ducks behind cover* cut out that step and just get out of the hardware business directly.

I would assume that he means that this time Nintendo should actually give more than a half-ass, token effort.  The Wii U was both weak and expensive, which is basically death for any strategy.

Still, that's not going to work with the current leadership.  I have no faith that they could compete with Sony and Microsoft on even terms.  They'd spend most of the budget on a hardware gimmick again, along with buying a couple third-party games.  That only way Nintendo succeeds in that market again is with new people calling the shots.

If they stay with Iwata and the Sunshine Band then they might as well stick with the current Nintendo fanbase as a target, only this time with a box that's cheap enough to be a viable "second console" and is very attractive to the family market.  Nintendo games don't need a lot of power while still looking very good.

Either go cheap or go strong.  Getting stuck in the middle will entice no one.

This!

A huge portion of that audience is from Japan where the console market is kind of dead. 

I agree with that last part, "getting stuck in the middle will entice no one", that's exactly what Wii U's problem is. Nintendo tried to get both the casual and mainstream crowd, basically trying to be a jack of all trades but instead failed on both sides, making it a console to play traditional Nintendo franchises but with its price and software output, even many Nintendo fans are content with just playing on 3DS instead.

Miyamoto said once that now they are going to focus on core gamers because casual gamers aren't loyal.

I've no idea but I'm sure I wouldn't like to be on Iwata's shoes right now. The pressure must be really high, just like the jump from GCN to Wii. The natural step is to keep Nintendo's identity always, now the way they'll make it happen I've no clue.

Core Market. End of story.