Learn Icelandic: Ókurteis samferðamaður truflar mann alltaf. - An impolite fellow traveler always disturbs one.

It is the direct object of the verb trufla (to disturb), which requires the accusative case. When the impersonal pronoun maður (meaning 'one' or generic 'you') acts as an object, it declines exactly like the regular noun for man: maður (nominative), mann (accusative), manni (dative), manns (genitive).

Since samferðamaður also ends in -maður, how do we clearly know who is disturbing whom?

Icelandic relies on grammatical cases rather than just word order to indicate this. Because samferðamaður is in the nominative case, it acts as the subject doing the disturbing. The pronoun mann is in the accusative case, confirming it is the object receiving the action.

Why does the adverb alltaf appear at the very end of the sentence?

In Icelandic main clauses, short object pronouns like mann usually shift to appear immediately after the conjugated verb. This pronoun shift pushes adverbs of frequency like alltaf to a later position than they would take if the object were a full, heavy noun.

Why does the adjective ókurteis lack a visible case ending here?

It is actually fully declined! It is using the strong, masculine, nominative singular form to agree with samferðamaður. For this particular adjective, that grammatical form simply happens to be identical to the bare dictionary word without any extra suffix added.