Not to sound snide, but please show me where they mention, show or talk about an actual traditional Tivo DVR. Tivo's cable setup is based on Android TV with Tivo Stream at its heart, not their traditional DVR software or boxes that we've been familiar with for ages.
<sigh> Various cable companies (including RCN, Atlantic Broadband and several others) have been deploying traditional TiVo DVRs containing CableCARDs for use with their QAM-based cable TV service for a long time now. In some cases, the versions deployed by those cablcos have looked and been branded the same as retail TiVos. In other cases, they have had different outer cases but contained pretty much the same internals.
Here's just one of many bits of evidence you could have turned up with a simple Google search. It's a story from 2014 by TiVo blogger Dave Zatz telling about how RCN had begun offering their customers a rebadged version of the Series 5 Roamio DVR, branded as "T6" for TiVo's cableco partners:
https://zatznotfunny.com/2014-05/rcn-tivo-t6/
You can see that it looks just like the retail Roamio Pro except it has the RCN logo on it.
A year or two back, TiVo got out of the business of manufacturing their hardware. In the traditional CableCARD line of TiVo boxes, it's Arris/Commscope who makes and brands those now. Their "MG2 Cable Media Gateway" is, I think, about at the same level as the retail Bolt for Cable DVR, with 6 QAM tuners, a 1 TB hard drive, and support for 4K and HDR10:
MG2 Cable Media Gateway | CommScope
The pics that you posted are from TiVo's new line of solutions for IPTV operators, which they brand as the
"TiVo Next-Gen Platform". Those are the boxes (sans hard drives, QAM tuners or CableCARDs) that run either Android TV Operator Tier or Linux. In either case, the UI is basically the same Hydra UI that's deployed on modern TiVo retail CableCARD DVRs, but with the operator's logo appearing. And, of course, the app selection varies. The version running Android TV Operator Tier has the Google Play Store app, giving users access to all kinds of apps that aren't available on other TiVo boxes.
What we're seeing in the story cited in the OP here is that three cable companies that have a long history of working with TiVo by provisioning their CableCARD DVRs to their cable TV customers have extended that relationship by now offering the completely separate TiVo Stream 4K device as an OTT streaming video solution for their standalone broadband customers. (In addition, RCN launched an IPTV service a year or two ago and they use the TiVo Next-Gen Platform for those customers. That's the thing cited in the first graphic you posted. I think RCN only offers IPTV on their new fiber-to-the-home network, which mainly serves MDUs, i.e. condo and apartment buildings. AFAIK, they still only offer traditional QAM-based cable TV on their traditional hybrid fiber/coax network, and still deploy traditional CableCARD-based TiVo DVRs there.)