Other databases are not supported at the moment.

There are several other excellent database storage engines, such as PostgreSQL and SQLite that WordPress is interested in supporting in the future. Supporting multiple databases is trickier than it sounds and is not under active development, although there are plenty of architectural discussions about the best approach to take. Approaches for increasing the number of supported databases are discussed at Using Alternative Databases. There is a PostgreSQL port of WordPress available called WordPress-Pg.