According to this:
I should be able to update Mac software from the
View menu of System Preferences. However, I don't see a Software Update option.
Here's what I do see:
etc... then ...
Has something changed?
I assume you're using an operating system greater than 10.7 (10.8 - 10.10)? With Mountain Lion (10.8), Apple moved the software update process to the Mac App Store application.
Prior to 10.8 Software Updates were handled in the manner the link describes. As such System Preferences had a Software Update section for managing timing of update checks.
Following 10.8 this is no longer found in System Preferences. Instead you should open the App Store and click on the Updates tab. Alternately the Apple menu has an option for App Store which, if updates are available, shows the number of updates waiting. (see picture)
The link you provide does not concern version of OSX where the updates are fully handled by the AppStore (OSX >= 10.8).
That being said, use the AppStore to update your apps :)