Translation:The doctor is at work.
I don't think the word contains location in its meaning. More like a state (the state of "being on duty for work"). For jobs done only at a designated workplace (such as office jobs where you can't work from home), the word will have the location implied. But the tips and notes say that the verb (근무하다) is used for soldiers like "to be on duty". Since soldiers don't do all their work at a designated workplace, I assume it doesn't necessarily have a location implied. You could also think about how a police detective on duty could be at McDonald's to ask questions of potential witnesses, or s/he could be off duty at McDonald's to get fast food. For a police officer, being described with 근무하다 probably doesn't say anything about where they are, just that they're on duty.
That may work much of the time, but not always. It's best to understand what "a(n)" and "the" mean/how they're used, what -이(/가) and 는(/은) mean/how they're used, and translate to whatever is best or most probable for the given sentences, but usually multiple choices for "a(n)" and "the" can be correct. It also depends on what noun is the subject or topic; for example, people's names and language names never have either "the" or "a(n)" added to them in English, so both 한국어는 and 한국어가 will simply be translated as "Korean" without any article. (Some languages like Italian often put the definite article before language names, but English doesn't. For example, 한국어는 어려워요 is "il coreano è difficile" in Italian where "il" is "the"--it is literally "The Korean [language] is difficult"--but in English we don't do that.)