On the shuffle, if you play the songs from the All Songs list, they will be in alphabetical order. If you want play them in playlist order, you need to switch to the playlist on the shuffle. You switch playlists on the shuffle using the VoiceOver button (press and hold).
This article provides instuctions for enabling and using VoiceOver
The part about switching playlists is in the sections Changing playlists and To choose an item from the playlist menu.
Even if you only sync ONE playlist to the shuffle, it still has a separate All Songs list AND that one playlist. In order to play the songs in playlist order, you need to play the songs from that playlist, not the All Songs list.