The library knows how to handle SQL to describe the work being done. The SQL is optional, one can, with the specification, read/write SQLite files in many other ways.
There are almost no RDBMS features in SQLite. There are many many other file formats that store data that offer features that are very similar to SQLite files: indexes, journaling, write logging, etc.
Thought question, you can ask a .tar file to give you a listing of what files and directories are stored in the file. Are .tar files RDBMSs? Consider:
1 - If you consider each file in the .tar file a "table" you can get list of tables.
2 - If each file follows a regular format, say JSON, you can search the "tables" by extracting the file and grepping it or using jq or whatnot.
3 - You can store a special file that is an index of some kind that lets you know in which file some data is, or even where in the file it is.
4 - You can build logic such that when you want to do other CRUD operations you can record a journal and a write ahead log to help build in ACID compliance.
5 - You can build buffer logic to support Write-ahead-logging, transactions and what not to improve performance.
Are .tar files RDBMSs? Trivially no.
But maybe, if you do all these things, you've invented a terrible database and database engine.
However, you need to build a server, user access controls, connection pooling, import/export tools, partitioning, clustering, etc. before you start to arrive at an RDBMS that uses this engine.