I'm assuming your shuffle is 4th gen (current model).
That first (leftmost) column, with no header and sequential numbers below, is the one you should have selected as the sort order (header highlighted). And make sure the small triangle "toggle" there is pointing UP. That should show the list in playlist order, from first item to last item.
I have my ipod shuffle set to manage music manually and not to automatically sync when connected.
If you are using the Manually manage music option, you need to create the playlist (using iTunes) on the shuffle, not in your iTunes library. To do this, it is easiest with the iTunes sidebar visible, so if it is currently hidden, from the iTunes menu bar, under View, select Show Sidebar.
In the sidebar, find the shuffle under DEVICES and select it. Click the small triangle to the left of the shuffle, to toggle down the iPod's content list. With the iPod selected, at the bottom of the sidebar, click on the plus sign and select New Playlist. A new playlist appears on the iPod's content list (indented under the iPod).
Load your playlist there. If you have an existing iTunes playlist, you can do a Select All on that playlist, and drag all the songs to the iPod's playlist. Make sure you drag the songs to the playlist indented under the iPod, and not to the "overall" iPod. Once your songs are there, select the playlist and make the playlist order as desired.
On the iPod (when you are using it), make sure you have the shuffle's power switch set to the play-in-order (middle) position. AND make sure you are playing the songs from the playlist, not the default All Songs list. Even if you only have one playlist on the shuffle, the All Songs list is not the playlist. If you play songs from the All Songs list "in order," they play alphabetically.
To select the playlist, use VoiceOver. This document has information about VoiceOver.
http://support.apple.com/kb/HT4322