Simple actually, since I see gyro aiming as something that standard classic controllers with gyro do very well - and that's (more or less) about it when it comes to gyro in them. They are still just a standard controllers that have gyro in them to augment some of the gameplay, but for full motion control play, they are just plain terrible or completely unusable. So for me that's just standard gameplay + some.
Sixasis was made with this in mind. Sony indeed pushed initially for this (mentioned Warhawk (which is good), along with Lair (not that good), both from 2007, are examples of that early push), to drop it then, revive it on Vita with Uncharted and Killzone, and then again mostly forget it, then revive it again lately - they definitely have the problem to stick with what they come up with. WiiU Gamepad is just a standard gamepad with gyro (and screen obviously). Switch, when playing Doom, Sniper Elite, BotW, Splatoon (where all this discussion started) is, in effect, mobile WiiU Gamepad, or when disconnected from screen, just a standard gamepad with gyro. So that's why I see playing those and similar games with gyro aiming as something that goes way back to Sixaxis and PS3 that tried to establish gyro aiming as standard, albeit, with no great success.

On the other hand, Wiimote (specifically Wii Motion), Move, VR controllers...they are made to fully support motion gaming (especially in VR, with all the advanced trackings, body, fingers...) and are focused on completely different experiences than sitting and gyro aiming and thus are vastly superior for actual motion gaming.

Yes, gyro aiming is technically a subset of motion gaming, but one that is very small subset and that was tried to be standardized first on PS3 (again, with no great success), without making it about full motion gaming that Sony later jumped in with Move, directly influenced by the success of Wii. Hopefully, this makes it clear why I see them as somewhat different, especially when it comes to who did first attempts at codifying them as standards.

At least 1.8 billion. There have been a lot of indie success stories on Switch and there are thousands of digital-only games.

DSiWare and WiiWare had very few quality games and neither service offered any kinds of discounts on games, so I estimate combined sales to be below 25 million units. This puts total DS and Wii software at ~1.9 billion.

There is still a flaw to your analysis. A lot of people who did not buy switch games bought Wii and DS games. These people bought ganes like Wii Fit, Nintendogs and brain age, games which sold half or a third as much on Switch. I will try to crunch numbers but it should be easy to calculate a few 100s of millions of missed sales.

For example, just brain age series goes like this:

There is still a flaw to your analysis. A lot of people who did not buy switch games bought Wii and DS games. These people bought games like Wii Fit, Nintendogs and brain age, games which sold half or a third as much on Switch. I could try to crunch numbers but it should be easy to calculate a few 100s of millions of missed sales.

My point is that the Switch sold gamer-centric games much more powerfully than usual, so they increased their performance on that segment. But had they not, the tie ratio would have been much lower. This means that the potential for Switch indeed was much higher than what we got. This means that the HW sales should follow this higher tie ratio leading to a much higher HW sales value. So the Switch most likely undersold hardware and software. But it's tie ratio is abnormally high for sure, this means that gamers bought more games on fewer consoles. It strengthens my point, as a normal tie ratio would mean the HW sales should be proportionately higher. Hard point to understand but it's true. Higher tie ratio really only means more games sold to a given console, it doesn't mean more players.

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Now I see the issue, you have a very questionable opinion about the use of gyroscopes in motion based gaming. There just plain terrible or unusable? Really? Gyroscopes have bad usage in Wii remotes and Joycons (non-traditional controllers)? I don't see how you can come to that conclusion. If anything you are grossly exaggerating their usage in traditional controllers. What is normal about using dual thumbsticks while tilting or twisting a controller? I literally turn it off when using my pro controller because it can be grossly uncomfortable. I don't want to remove the option from you but acting like the best usage of gyroscopes are in traditional controllers is a wild take. Especially when clearly this can't be a popular opinion when Sony ditches them and Xbox doesn't offer them at all. Nintendo only pushes it because of Splatoon. 

Gyroscopes best usage are definitely in motion based gaming and go extremely well with non-traditional controllers like the Joycons because I'm free to twist and tilt the controllers independently. Gyroscopes have great usage for sports based motion based gaming, tilting or twisting to emulate a tennis racket,  or control my spin in bowling. Even gyroaiming with my Joycons feels natural because they are independent, I literally aim my joycons like wii remote because it feels natural. I personally would rather use gyroscopes for gestures in Call of Duty like maybe to roll when fully crouched? 

Like seriously, this is why you are so interested in separating gyroaiming from motion based gaming, it's because you have a very strong opinion of gyroaiming. It clearly isn't that popular and gyroscope usage is far more popular in motion based gaming. Gyroscopes are used in multiple different ways including gyroaiming and motion based gaming. Which why me and Curl view it all under the same umbrella.

Honestly, I have no idea are you trying to misinterpret what I say, or you just don't understand, so I just leave it at that.

Yes, gyro aiming is technically a subset of motion gaming, but one that is very small subset and that was tried to be standardized first on PS3 (again, with no great success), without making it about full motion gaming that Sony later jumped in with Move, directly influenced by the success of Wii. Hopefully, this makes it clear why I see them as somewhat different, especially when it comes to who did first attempts at codifying them as standards.

I certainly wouldn't call it a small subset given it makes up a very substantial portion of the games on Switch that feature motion.

Serious question; how many PS3 games actually feature gyro aiming as it appears on Switch? Sixaxis seems to have been largely used for things like steering/balancing, which Wiimote did too. You tilt to play in Excite Truck, a Wii launch title, and in several other games dating back well before Sixaxis. 

Not sure really, not a lot. In Warhawk you steer with it and guide some missiles. In Heavenly Blade you guide arrows. Not sure for other games.

Excite Truck was fun. Somewhat similar, but not quite the same thing, since original Wiimotes don't support 6DoF (like later Wii Motion Plus).

Like I said, when I see game played with standard industry controller with gyro aiming (or something that resembles it, as in case of WiiU and Switch, when you use it to play games we talk about here), my mind goes back to Sixaxis, not Wiimote. Cause you can't pick up Sixaxis and play something like Archery or Tennis on PS3. You need to sit down and play your gyro augmented games - that's all it's good and intended for, unlike Wiimotes and by extension Switch controllers where you can play all those get up and play games as well.

I can see we'll never agree on this one, so honestly I don't really think there's any point further discussing it and hogging up original topic.