Reason for A and el in this sentence

Hola Shirley 

¡Muy buena pregunta! 

First of all, we use the article "el" in "el deber" because we're using this as a noun, although it looks like an infinitive and it may be confusing to see that, but that is in our lesson "Using Spanish infinitives as nouns" - other examples of using an infinitive as a noun could be: 

El fumar tanto te matará un día. 

Smoking so much will kill you one day. 

El abrir y cerrar de puertas no me ayuda a concentrarme. 

The opening and closing of doors doesn't help me concentrate.

Then, the use of the preposition "a" in "A este soldado..." is linked to the verb "llamar". Llamar can be used in this context of "attracting someone to do something", so, in this sentence it is like saying that "duty is calling him as in he is attracted by this feeling of duty". In this case, you need the "a" when mentioning the person who is attracted, functioning as an indirect object. If you have a look here on the different uses of the verb "llamar" by the Diccionario de la Lengua Española, you can see this same use in number 10 with the example of the chocolate. 

I hope this clarified your doubt.

Un saludo y felices fiestas

Inma