I think this one was chosen to show the difference between Esperanto and English. In Esperanto the direct object is marked by the accusative n and can be anywhere in the sentence. In English the direct object follows the verb.
In normal use this word order can put stress on the passport or to have the word diplomato at the end position for the easier use of an following relative subclause. But you can it use also because you like the rythm of the sentence more or it is nearer to the word order you would use in your native tongue. Feel free.
I like your point about a relative clause easily following the subject! I hadn't thought about that.
It's not used often, and you don't need to use it, but you should be able to recognize it. A word order like this is possible because the accusative case (with the -n ending) still shows you what the object of the sentence is. That way, you know this means "the diplomat has a passport", not "a passport has the diplomat". So it's important to keep an eye on the endings of words - sometimes sentences can be sneaky like this! :)
Languages that mark case usually have freer word order and word order can be used to subtly highlight various parts of the sentence. Surrounding context also affects it.
If it's anything like doing the same in German, it's for emphasis. (der Hund beißt den Mann: the dog bites the man; den Mann beißt der Hund: the dog bites the man)