Why does Office for Mac need Safari and Chrome closed for installation?
Presumably, the Office installer can modify/update the Microsoft Silverlight.plugin (which is installed in /Library/Internet Plug-Ins/), which Safari and Chrome could potentially be using.

It's primarily just a precaution against updating files which an application is actively using.

[EDIT]

After further investigation, it looks like it's actually the fact that the installer modifies the fonts in /Library/Fonts/Microsoft/ which is the motivation behind requiring that several apps not be running. The following is an excerpt from the XML Distribution script that's in the 16807Office 2011 14.3.5 Update.pkg installer package:

&lt;choice id="fonts" selected="true" start_enabled="false" start_selected="false" start_visible="false" title="fonts-title"&gt;
    &lt;pkg-ref id="fonts"&gt;
        &lt;must-close&gt;
            &lt;app id="com.apple.Safari"/&gt;
            &lt;app id="org.mozilla.firefox"/&gt;
            &lt;app id="com.google.Chrome"/&gt;
            &lt;app id="com.operasoftware.Opera"/&gt;
            &lt;app id="com.microsoft.Word"/&gt;
            &lt;app id="com.microsoft.Excel"/&gt;
            &lt;app id="com.microsoft.Query"/&gt;
            &lt;app id="com.microsoft.Powerpoint"/&gt;
            &lt;app id="com.microsoft.Outlook"/&gt;
        &lt;/must-close&gt;
    &lt;/pkg-ref&gt;
&lt;/choice&gt;


[EDIT]

Another pair of potential culprits are 

SharePointBrowserPlugin.plugin
and
SharePointWebKitPlugin.webplugin 


They are installed by default with Office 2011 under /Library/Internet Plug-Ins. (Note: Silverlight was not an option to install with 2011).