The crucial distinction as far as the OP is using the term seems to be that such a datastore does not require the user's hosting provider to give them an instance of any of the common DB servers, which typically needs a more expensive plan than the usual baseline of "disk space and an httpd [that supports calling out to one or two scripting languages]".
(Basically it should run on anything more complex than a static site host. Though it's also true that sqlite would probably be a cleaner choice for the datastore without losing any of that benefit.)
SQLite would be nowhere near the current design in term of performance. Typical shaarli usage involve little update (a dozen a day maximum) an a lot of read (10k+ pages viewed per day on sebsauvage's instance (shaarli's creator, an influent french blogger). Thé file system's cache works really well in this kind of scenario, way better than SQLite.
For the stability guarantees, shaarli exists since 2011 and is used in production by many (several hundred) people without trouble.