Or it could be an NX launch title releasing late 2016/early 2017 with the PS4 version ( which I expect will be delayed.) From what we can tell though, SE wants to support the NX. Otherwise they would have said nothing about it.

SE wants to support the 3DS and that much is certain ...

Depending on what NX is, don't be too quick to claim the same will happen with NX when EA and the of the others ditched the WII U despite their words ...

How could a NX version, currently in debate within the company on whether it could be profitable or not, possibly release at the same time as the PS4 version on which entire dev teams are working tirelessly as we speak?

Sure, but even EA released some Wii U games at the beginning. Also Square-Enix knows how to deal with Nintendo and get them to do odd things (like publish their games.) EA was having trouble getting Nintendo to allow Origin on Wii U.

As I said, I expect the PS4 game to be delayed. It looks like it has been barely worked on, and DQ games always seem to be delayed. If NX is a home platform there is a good chance it will have an X86 architecture and an NX port could be a priority in the last few months of PS4 development. It's weird that SE would even mention NX unless they know something about it.

Just think for a moment, why would they announce publicly that they are considering to release on NX if Nintendo fans can play the game on 3DS? What benefits do they get to just "consider" it?

NX will be shown until next year.

Nintendo.

Showing this winter will take away sales for the last holiday season of 3DS and Wii U.

That will be another terrible mistake from Nintendo. Iwata's lasts comments hints towards a reveal and release the same year. Same thing happend before with 3DS and DS.