I don't understand this part. Aren't they portable consoles? Are you disputing the "portable" or the "console" part? The technical term is handheld game console, usually shortened down to "handheld" but they're still consoles, if that's the disputable bit. And they're inherently portable in the sense of "easy to carry around with you".
I believe this illustrates my point: if you google "portable console", you get this. Or if you want to rule out handhelds, you can try specific names, "portable Xbox", "portable Wii", "portable PS2", it gives you a ton of case mods and mockups of portable versions, and they all have screens.
I'm not saying the GameStick isn't portable as such, I'm just saying that the word, when talking about consoles, usually implies a screen.
Well, I think that harkens back to what I talk about when we muddy the language, things become more amorphous. If you google "console" handhelds don't appear, if you google "handhelds" consoles don't appear. There is not a person who would understand "console" unqualified to include handhelds or vice versa (at least not in general usage). It's easier to stick with the differentiation that is most commonly understood. If we want to use lesser utilized methods of referring to technology we could refer to consoles as "video game consoles." (Your wiki link does use the term "handheld game console" but the wikipedia article for "video game consoles" says that, "[the term "video game console" is used to distinguish a machine designed for people to buy and use primarily for playing video games on a TV in contrast to arcade machines, handheld game consoles, or home computers." So the video game console, generally shortened to "console" is a moniker intended to differentiate it from other similar devices like handhelds. In short they were shortened to "console" and "handhelds," so the use of the term console is important and distinguishable (at least in common usage).
I entirely agree that there is no real quantifiable difference in the experience and that one could easily be the other, it's just not how the words are generally used.
So once we set up that dichotomy, would it not be more appropriate to say the portable version of a device that is emulating the characteristics of the former (anchoring to TV being the biggest one) is a portable version of the former?
A console you can pop into your pocket, but requires a screen doesn't seem like a handheld--it seems far more like a console...just a portable one.
The implication of the screen is something I can't readily refute and you're exactly right on that. It does generally imply a screen--as seen in many portable versions of consoles--but that is not an exhaustive way of looking at it. There is no "general" view of what the game stick is it does not fit in with the definition of a handheld device.
Since it fits neatly into Wiki's definition of video game console wouldn't it be easier to say a far more portable version of that is a portable console? That way we can continue to use the commonly understood distinction between consoles and handhelds that we've had since we've started using the terms in common parlance.
It is clearer that way to me, anyway.