To clarify something to inexperienced people most of the so called '' fake'' nintendo ds systems sold are NOT FAKE, they are REFURBISHED.
Yes there is a GIANT difference because REFURBISHED system are able to play retail nintendo ds games just fine on top of that they use an ORIGINAL NINTENDO motherboard. I know this because i repaired a great number of these systems and i know the difference between refurbished, brand new and ''fake''.
In fact the ''fake'' models will not even play nintendo ds games instead they play gba, gamecolor and other emulated games its just the design that looks similar to nintendo ds lites and UI.
To answer your question: nintendo ds lites are quite rare now, even if most stores have them which are not known large retail stores they are probably selling refurbished units.
I don't recall a royal gold color ever being released other than the zelda limited edition one in North America but i could be wrong.
If you want to really verify you would have to open up the back of your system and check the actual motherboard, another indication would be the battery too, most refurbished units have 3rd party batteries.
If your unit is really reburbished would it be all bad? There is nothing wrong with a refurbished unit in most cases, and they work just fine on top of that the specific color you got is kind of unique. The only thing i would worry about is the 3rd party battery if it is one, because those don't last as long as the original ones.
I would be cautious on opening the back of the system to check the motherboard though, as its somewhat easy to break off your power switch when putting the bottom back cover on again.
My guess is its probably refurbished, the serial number kind of gives it away and the whole box thing stating the 3ds part is even further evidence. You do realize these systems were released years before there were any 3ds games right? After seeing the pictures i am somewhat sure that if you unscrew the battery cover that you have a 3rd party battery.
so in a nutshell , yes i do believe you have a REFURBISHED nintendo ds lite system