For the first part, I completely agree, however, I don't think they stopped caring. Sony never cared, Nintendo, MS and Ubisoft cared to the bitter end. Nintendo even built their Wii U in parts around offering that audience an interesting follow-up. With NSMBU, Wii Fit U and Nintendo Land as (near-) launch titles it's obvious they did care and wanted to get that audience again. They failed though. Even with the 3DS, they had Kawashima and Nintendogs reappear, but here they it was quite obviously an afterthought. Microsoft bet on the new found audience, too, with the heavy investment in Kinect and media functionality that furthered the success of the 360 in its final years. Ubisoft tried, both, on Wii U and Xbone, to target the new audience with games like Rabbids Land, Just Dance (ongoing) and that Fighter gamer on the Bone.
Ubisoft is probably the one who served that market the best actually, Just Dance is still selling and there never was any gap.
MSFT never ever cared, they stopped making software pretty early on, once it was time for the xbone they pretty much stopped their plan to cater to the expanded and tried to take people who watch tv instead for god knows what reason.
Nintendo stopped caring circa 2010, they thought that their new audience cared about their legacy IP more than they cared about the product they sold.
That's why we got Nintendo Land to celebrate their IPs after all, if you never touched any Nintendo product and got on board because of the DS or Wii's expanded audience products you're never going to anticipate something like Nintendo Land.
It took more than a year to brind about WiiFit and Sports on WiiU when the market was cold anyway.
The IPs they created on as evergreen mattered to a point, 3DS and WiiU were just to hostile to that market to make any dent.
It's pretty much why outside of licensed products most 3rd parties can't seem to sell to non gamers even there's 1 product trying to.
Also that audience got literally nothing to play between 2010 and 2012 anyway, they weren't going to wait for ever.
NoA did also a good job trying to kill Wii itself by simply refusing to release anything NoE had in the pipeline while putting all its eggs in the Zelda basket.
They did care, but there were two things that prevented this from working out:
1. Misreading the market and approaching the audience with too many "follow-up" type games instead of completely new experiences. The one completely new experience for this market, Nintendo Land, just failed to catch on, maybe because it was a bit too gamey in presentation - though it is a good product.
2. The rise of free or almost free games on Facebook, as well as on phones and tablets swayed a lot of people in that segment away from traditional consoles and made the market for Nintendo's Wii-type experiences and Kinect shrink significantly.
Unless you never played Facebook games, Wii games and Kinect games you can't exactly conflate the 3 like that.
Kinect died because there never was anything that interesting to do with it, outside of Dance games I'd argue that there was little that could survive the novelty anyway. the market wasn't going to stay there anyway (as evidenced by MSFT inability to make anything compelling for it on the xbone).
Wii type died because they stopped making them, the market sustained it for nearly 4-5 years, when they stopped making it they stopped selling.
Nintendo trying to distance itself from Wii's strategy with WiiU and its lineup meant that the audience wanting more Wii was never going to be interested in WiiU's initial proposition.
Facebook games offer similar experience to mobile games, that market moved on to mobile entirely. Outside of some DS games there's really nothing in common with mobile/facebook games and the type of software you find on dedicated machines in term of commitment, value proposition and type of experience.
I'd argue that they could survive alongside (like mobile/dedicated machine are doing or pc/console always).
If the former expanded market left the dedicated gaming systems to mobile/facebook, it has more to do with how they weren't being served by dedicated gaming system more than mobile replacing it.