Josh Kelley's answer is so far the BEST answer ever I've found about the reason of the standard work to be stopped. That said, I think there is an additional perspective to consider regarding the user-base.
Eventhough, I disagree on Ido Green's approach to the subject ("This is a recommendation for web developers to no longer use the technology as effectively")...
I believe (as vi4m states in the comments of Ido Green's article):
We (developers) can still use this technology. No browser vendor requested removal of this technology, nor plan to remove it. Developers are the voice of the web. We can just still using it, maybe Mozilla will change mind ;-)
And I would add another logical approach: If you are developing for mobile ambient... ¿what ambients are in more hands? Answer: iOS and Android...
So if BOTH support webSQL, and your target is MASSIVE MOBILE, go for it!
Think as big apps have done almost always at the beggining, get the MOST first, then (once achieved success) recreate the work to get the remaining less (if you really want to achieve them or are asked to do so). Finally, ins't always success who marks the path?
After reading Nolan Lawson's article (in which is clear his intention to give a chance to his invention) I believe this matter became a new cold-war between tech-giants that shouldn't even exist.
I believe specs are made to stay (as -longer and untouched as possible- the better for client oriented performance). Ironically the "specs guys" job is to generate NEW specs (sometimes where there is none needed, so he can have something more to do), and likewise programmers jobs sometimes focus on changing and rewriting what already works instead of doing solutions for new problems and new tendencies.
For me, Client-Side Databases was a matter of simply making parallels (between server and client sides) so we could create, store, upload and download data easily. Under this approach, having the same languages and structures (at least for us, LAMP opensource developers) is straight forward and logic.
I believe IndexedDB intention for being an alternative with wider and newer possibilities is an always good approach, but somehow it resembles for me to the need of developing software that NEEDS to be installed (even when the core solution can stay on the cloud). In a world that tends to stay connected it sounds like A) a matter of control and possession or B) focusing on developing monsters for the client-side... but for those kind of needs exist Apps (in the Mobile world) and software (in the PC world).
I believe the goal of Webapps should stay mainly on extending the web no matter the device.
I believe a nice infographic could come out of this approach.