The irony, of course, was that it turned out that if you used PostgreSQL and simply stored json in it, you could get better performance without giving up on a relational database... and even more damning was that the translation from MongoDB's query syntax to PostgreSQL's query syntax was trivial, leading to people building adapter layers that were drop-in compatible (and yet still faster and safer than MongoDB). So I guess there was something fitting about seeing someone post a project that is trying to the SQLite of MongoDB, but with benchmarks right off the bar showing it slower than SQLite ;P.
I thereby continue to feel that if you want to use MongoDB, but want a library version of it, it would seem--based on this project's own benchmarks, unless you are doing a read-heavy workload of random documents by index--that what you probably want is a query translator to go from MongoDB's syntax to SQL (working with the SQLite json API), and then store your workload in SQLite... which is (critically) a battle-tested production-grade database engine used as a foundational storage layer for lots of projects.
That said, it isn't like SQLite was a drop-in replacement for other database engines: when I think of "X is to SQLite as MongoDB is to PostgreSQL" I picture something that is attempting to being benefits over SQLite -- in way of performance or scalability -- at the cost of losing the power of being a full relational database (and, because of Mongo's legacy, probably a lot of safety and stability guarantees ;P). (FWIW, I remembered there's being a project like this: UnQLite-- https://news.ycombinator.com/item?id=18101689 --where people ironically seem to have wanted to get it benchmarked against SQLite with its json API ;P.)
It sounds like maybe this project is just trying to provide MongoDB's query layer? You simply don't use SQLite until you "migrate to the full PostgreSQL"... they are designed for different scenarios, and while SQLite is good enough you might be able to use it in a place where PostgreSQL "was called for", a migration might be brutal (as the syntax and type system are different). The project tagline is thereby leading to the wrong mental space--as seemingly multiple other people have since now mentioned on this thread--particularly given that it is written in Python.