why it appears MySQL is ...
Appears to whom? Appears to you? Only you know that.
In security there is no "appears". Either particular attack is possible or not.
Nothing in this whole video shows any weakness of any database. SQL injection is a problem of the application code, not the problem of particular database.
To error-based SQL injection: If the application catches all database errors, then the attacker will not see any details and thus this attack will not be possible. The speaker showed some examples of what data can be retrieved via error messages. I suppose that he didn't see anything more to add to it. Where as for two other types there were more scenarios possible and the speaker provided more details about them.
Once again: databases are NOT vulnerable to SQL injection, but applications.