Yeah I also noticed that he seemed weirdly excited to announce the arrival of the third client. I want to hear more of the story behind this.
Perhaps the third client does not get along with the first two, and there will be brawl.
I really had no idea what the sentence was trying to say. I wrote, "The client is the third in the building." Was there something in the case endings that could have helped me?
Tertius, tertia, tertium is an adjective, meaning "third." The noun "cliens" is masculine, so with the adjective, it becomes "cliens tertius." So the third client is in the building.
However, I can't guarantee that this couldn't be interpreted with a nominalized adjective, in which case your interpretation would actually be correct. I'll let someone else weigh in on this for the time. :)
Volgav vitsenanieff nivya kevach varatsach.