Using dynamic SQL in a query, as per derobert's answer, is the only to do this with pure SQL (no app code).
I wrote a generalized procedure to do this sort of thing (run a query for every table in a database) that you can find here - to use it, you would just need to run this query:
CALL p_run_for_each_table('databasename', 'DROP TABLE `{?database}`.`{?table}`');
It works in essentially the same way as derobert's answer.
However, the writer of that blog post was probably expecting you to write app code to turn the names of tables into a single DROP statement.
To do this, you would iterate over the results of the SHOW TABLE in your code and build a single query like this:
DROP TABLE table1, table2, tablewhatever;