The main things you need to be careful about if you want to just try dropping a new Omeka version on top of the old one are:
- overwriting things like your configuration files (db.ini in particular comes to mind)
- leaving around old files that have been deleted in the newer version of Omeka
- overwriting any Omeka core files you may have edited
If you're careful about making backups of your config files (or the whole installation) so you can restore them, and if you haven't been editing core files, it should be pretty safe for you to just install the new version on top of the old. This is especially true when you're switching between different maintenance releases in the same series (1.4.1 to 1.4.2) since those usually have more minor changes.
All that being said, the instructions you linked to on the Codex are still the recommended procedure. The idea is to make sure everything's safely and correctly updated for different circumstances.