So basically the setup for this phrase is more passive, and similar phrases are used in Italian in Spanish.
It means "you are missing to me" hence tu (subject) me (object) manques.
In terms of "je pense à toi" you typically say "je pense à" + object ... so "I am thinking of the books" is "je pense aux livres"
So that's why you need the "à" -- it's a set phrase for how to say thinking about rather than a simple direct or indirect object.