Reading through
https://www.sqlite.org/releaselog/3_26_0.html which they linked to, I'm presuming that it is tied to items 3 and 4. Which is highly suggestive that the problem is that ordinary SQL is able to write to internal virtual tables in a way that corrupts the database. And presumably from there, once you can introduce corruption you can get it to exploit a payload that you provide.
The fact that Chromium also saw fit to patch this suggests further that there was likely some way that it could be tricked into issuing queries that did this, allowing some compromise of the browser. If this could have been triggered by a web page, then that explains why they are light on details.
It should be noted that a lot of applications embed SQLite internally. If one as well studied as Chromium could be tricked in this way, I'm sure that others can as well. And since the upgrade has to happen to an embedded component, we're probably going to hear about this one for a while.
Please note, this is all educated guesswork from knowing the software ecosystem and reading release notes. I have absolutely no knowledge of the vulnerability.