Is there an open-source SQL database that has the concept of Oracle's "rowid" pseudo-column?

PostgreSQL does have this concept.

See here for a brief list of pseudocolumns in PostgreSQL, out of which ctid is of interest to you:

ctid (tuple identifier)

The identifier which describes the physical location of the tuple within the database. A pair of numbers are represented by the ctid: the block number, and tuple index within that block.

That is direct analog of Oracle's rowid.

As for MySQL, physical location of a row is not available for the front end.

In MyISAM, rowid is just a file offset from the beginning, and that's what is stored in the index leaves.

In InnoDB, tables are index organized by design, that means they always have some kind of a primary key, and the indexes over an InnoDB table use that PRIMARY KEY as a row pointer.

This is also true for Oracle's index organized tables, for which a rowid is not a physical pointer to a block in a datafile, but rather a such called logical ROWID, or UROWID

If you select a ROWID from an INDEX ORGANIZED table in Oracle, you will see that it has a different format (something like *BAEBwPICwQL+). This is in fact an encoded PRIMARY KEY value.

Note that if you have not defined any column as a PRIMARY KEY, MySQL will create a hidden surrogate PRIMARY KEY over which you will never have any control.

That's why you should always create some kind of a PRIMARY KEY in an InnoDB table: it's free, and you get control over the column.

if neither of them have done that, then no others do.

SQLite has an auto incremented "ROWID" column which you can access using ROWID, _ROWID, or OID. If you define an integer primary key than they will be aliased.