I found an answer to my own question. I am running Office 2010 ("version 14.x"). To enable updates again proceed as follows:

1. Close all running Microsoft Office components.
2. Open Regedit
3. Go to HKEY_CURRENT_USER\Software\Microsoft\Office\14.0\Common\General
4. Modify the "ShownFirstRunOptIn" value from 1 to 0
5. Launch a Microsoft Office component, it will give you the option to download the updates, make sure you select it.
6. Done. If you go back to "Windows Update", then "Change Settings", you will see the "Microsoft Update" and "Software notifications" sections are available again (until the Microsoft Update check box is unchecked again).

The key in step 4 might have slightly different names across office versions. In my source the key was called ShownOptIn under office version 12.

Following these steps also MSU shows the missing checkbox again and it finds all updates including updates for non-office products (e.g. Silverlight)

Verify or install the latest updates

You might have to set Windows Update to automatically download and install recommended updates. Installing any important, recommended, and optional updates can frequently correct problems by replacing out-of-date files and fixing vulnerabilities. To install the latest Microsoft Office updates, see Update Office and your computer with Microsoft Update.

For list of the latest Office updates, see Office Updates. If your issue is not resolved after you install the latest Windows and Office updates, go to method 2.

It's a good idea to make sure that your computer has the latest updates installed for Windows. Updates often fix software problems. Before you use any of the following methods, try first to install updates. After you install the updates, restart your computer, and then start Word.

Troubleshoot problems that occur when you start Word

Important
Follow the steps in this section carefully. Serious problems might occur if you modify the registry incorrectly. Before you modify it, back up the registry for restoration in case problems occur.

Here are troubleshooting methods you should try:

Method 1: Insert your document into another file
Method 2: Start Word by using the /a switch
Method 3: Delete the Word Data registry subkey
Method 4: Delete the Word Options registry key
Method 5: Replace the Normal.dot or Normal.dotm global template file
Method 6: Disable the Startup folder add-ins
Method 7: Delete the COM add-ins registry keys
Method 8: Change the default printer

Follow details in MSDN.