Windows 8 Why can't my friend access his Windows 8.1 Start Menu Like Win 7?

That attachment of the navigation tab is not from windows 8.1, it may be from windows 8. That said, uncheck the box use apps first and the check the box to use desktop mode on start up. Now you have to apply (save) those changes in order for them to take place.

Here's mine.....

P.S. the one you circled in red is only about whether you want background picture to be used on Start screen. If it is unchecked, Start screen will show default solid color as background ( mine is blue.)
It has nothing to do with "start menu".

I use the Desktop rather than the Apps screen as follows:

1. Put a Shortcut to the Start Menu on the Desktop by navigating in File Explorer (was Windows Explorer) to the hidden folder C:\ProgramData\Microsoft\Windows\Start Menu, right-click or press and hold Programs and click or tap Send to (Desktop shortcut). You may have to tick ‘Hidden items’ in the View Ribbon of File Explorer.

2. Put a shortcut to msconfig on the Desktop to give you access to about 18 programs on its Tools Tab, including regedit, event viewer and system restore. Navigate to C:\Windows\System32, right-click or press and hold msconfig.exe and choose Send to (Desktop shortcut).

3. Further programs can be accessed by pressing the Windows Logo key+X (or right-click or press and hold off the bottom left corner) and choose from a list. The full list is Programs and Features, Mobility Center, Power Options, Event Viewer, System, Device Manager, Network Connections, Disk Management, Computer Management, Windows PowerShell, Windows PowerShell (Admin), Task Manager, Control Panel, File Explorer (was Windows Explorer), Search, Run, Shutdown (Restart, etc.) and Desktop.

napninjanx,
Should you or your friend change mind and decide to try out some 3rd party Start Menu programs, here is a list of FREE programs :
Bring back the Windows 8 Start button with 6 free apps

Personally, I use Start8 by Stardock.
It's $4.99 one time purchase.
It works just like Windows 7 Start Menu. If you stick with the desktop, you would have thought you were on a Win 7 computer.
Start8 returns the familiar Start menu to Microsoft's latest Windows 8 operating system.
This is how it looks like. Screenshot was taken before I had Update 1 installed.

If Win 8.1 shows a start menu like Win7, it would have been so sweet. What is wrong with 3rd party app?
I don't know if someone mentioned it already, I am using Classic Shell (I think most people does). Very customisable.