"My parents like beer."
Translation:Ai miei genitori piace la birra.
It took me a while to get further down the skill tree to the Clitic Pronoun section to actually understand what you're saying here. You're right; you could use an indirect pronoun before "piace" and you wouldn't need the "a." (Mi piace, ci piace, gli piace, etc.) However, indirect pronouns include the "a" within themselves. So "Mi piace la birra" is the same as saying "A me piace la birra." Both translate into "I like beer," or more literally, "to me, beer is pleasing."
Because of the way piacere works, you have to start off saying "To the object of the sentence..." and in this case, "ai miei genitori" means "to my parents." The "a" is necessary for it to make sense. Without it, you are saying "My parents, beer is pleasing."
You could also say "Gli piace la birra" to say "They like beer" and you wouldn't need the "a," but that's for a future lesson anyway. :)
In your first example, "I miei genitori" is the subject of the sentence.
In the second case, however, "birra" is the subject and "i miei genitori" is the object of the prepositional verb "piacere a" and, since the preposition "a" combines with the article, you get "
ai miei genitori".