Yes, I'm not sure why they are not putting the mark for this vowel. Anyway, this -un sound is called Tanwin or Nunation (you can check Wikipedia for it).
This type of vowels (which can come in other flavors, as -in and -an as well) is used in a number of occasions. For the time being, you can think of it as the sign for the indefinite noun and adjective; Somehow like the English a/an before an indefinite noun. So, the above sentence should be رَجُلٌ أَمْريكي (rajulun amríkiy"yun") - the last -un sound can be dropped when the word comes at the end of the sentence and there is no continuation of speech after it.