Well, I thought that I came here for the chicks, but since you ask.......

I would say that it is something entirely removed from the black-and-white of attaching it to a generation. Timing-wise, it would be something more like Generation 8.5.

You want to go definitions here

"A handheld game console, or simply handheld console, is a small, portable self-contained video game console with a built-in screen, game controls, and speakers.^[1] Handheld game consoles are smaller than home video game consoles and contain the console, screen, speakers, and controls in one unit, allowing people to carry them and play them at any time or place.^[2][3]"

The Wii U's portability doesn't fall under this no matter how hard you want to loosen the definition of portable you know why? Because it's not self contained and can't be play anywhere therefore it's not a hybrid Handheld/Home Console as it can only be played at home no fallacy or loose definition you pull out will change this fact.

So the Wii U isn’t a hybrid because you can’t use the gamepad without the main console. So it’s a standard home console.

So logic would state that the Switch isn’t a hybrid because you can’t play with the dock without the handheld. So it’s a standard handheld console.

Hybrid is just a buzz word, I guess.

Either that or they are both hybrid consoles despite one having bigger limitations. No where is it said that for a console to be a hybrid, it has to be handheld first, home console second. Both the Wii U and Switch achieved their hybrid form factor with opposite method. One being a home console first, the second being a handheld first.

But of course, Nintendo mentioned that buzz word only for the Switch... 

Except you can play on a TV with out the dock as I mentioned earlier so your attempt at a fallacy hilariously falls apart as Switch is fully self contained, what further highlights how laughable your attempt at trying to save this sinking argument is that the definition of a hybrid would mean that the device has to fall into the definitions of both handheld and home console and guess what Wii U doesn't fall under the definition of handheld so therefore can't be an hybrid as the device is rooted to be played only in the house while Switch comfortably falls under both definitions. You have presented no argument that counters this hence the failed fallacy attempt.

What a hilarious reply you laughably wrote there. Couldn’t refrain myself from chuckling at this complete display of hilarity.

I mean, seriously.

So... The Vita is a Hybrid console. Thanks for clearing that up.

Ironic considering the only other person who shares your view dismissed Vita as we brought that up against both your views and even he said it doesn't fall under that as the PS3/4 is required so this leaves you hilariously on your own in trying to be funny, don't worry we all laughed at your poor attempt at posts as well here's a simple question for you, can Wii U be played anywhere as described in the definition or a portable handheld above?

Simple yes or no answer.

It's not our argument that the Vita is a hybrid console.
So do you believe it to be a Hybrid console or not? If not, then why?

Earlier me and some others pointed out that under the notion you're pushing it would make the PS3 and Vita hybrids because of remote play but you said that's entirely different as they're separate devices that require each other which is the point in the reply to him.

If by Switch I've always said it's a hybrid that has access to both portable and home markets if you mean Wii U no it's not a hybrid in my view because being limited to one location doesn't make it a portable it's just a home console with a convenient feature.

That isn't what I said at all. I suggest you go back and re-read my statements if that is the conclusion you came to.

The WiiU does off-screen gaming. Each and every single console does that out of the box.

List the amount of fixed home consoles that you can game anywhere in your home without the requirement of a Television.
It can be used as a handheld or it can be used as a traditional console gaming device. - THUS by it's very definition it is a "Hybrid" device as it melds two different concepts together.

Thus far I haven't been shown an argument that is really solid on why the WiiU isn't a hybrid.

"The Vita is a separate console, not an accessory that is included with every single Playstation 4 sold, meaning we cannot regard the Playstation 4 as a hybrid device as not every Playstation 4 came with everything out of the box. (Although, Sony would probably appreciate the extra Vita sales.)"

That's the vita/PS4/PS3 part sorted, look at the definition of handheld I linked you earlier Wii U doesn't fall under that as you're rooted to one singular location your home while a handheld by definition allows gaming everywhere so by that definition Wii U is not a handheld much like the same way a cordless house phone is not a mobile phone as a result Wii U is not a hybrid. As for your question PSone and PS2 had screen attachment accessories that allowed gaming with out TVs.