I too get the same error for this exercise. If you click on the error message banner it will give you more details of the error. For me this gives...
Errors: ERROR: 1 new attribute(s) not added
SQLite error: duplicate column name: AREA
SQL: ALTER TABLE "landuse" ADD COLUMN "AREA" FLOAT
It appears that the supplied "landuse.sqlite" file in the exercise data is in a confused state: if a connection is made to the sqlite database within QGIS(2.6), then the database is examined via menu Database -> DB Manager -> DB Manager then selecting "landuse" within the database, it can be seen that a field called ACCESS already exists. However, if this layer is loaded into QGIS via the "Add Spatialite Table" button, an examination of layer properties->fields or just opening the attribute table will not show the field.
(Starting with a new copy of landuse.sqlite), if a different column name is added "AreaV2", then the hidden "AREA" field suddenly becomes visible and a different error is generated...
Errors: SUCCESS: 1 attribute(s) added.
ERROR: the count of fields is incorrect after addition/removal of fields!
Note: this is using data taken from the official download location...
Perhaps when the database was created the "AREA" field was deleted after testing, but the deletion method only partially worked?