The problem was that with that particular SQL update, if you look at it, the third query is "UPDATE auctionhouse, mangos.creature AS c, mangos.creature_template AS ct..." If your world DB isn't specifically named "mangos", this query and the rest of the update will fail. However, since this is after the "ALTER TABLE character_db_version CHANGE COLUMN required_..." part, mangos will still run fine.
To fix it, I just copied the update into the phpMyAdmin SQL tab, removed the first query and the second query (because these parts had already been run) and just changed "mangos" to the name of my world DB. Ran and worked fine.
@ Mangos developers: the next time you need to make an assumption like this in a SQL update, can you please check that the other DB is named what it is assumed to be? Or at the very least, use a SQL transaction so when it fails it doesn't leave the DB in a state of half-update.