Both (all three) are neo-classical.

No.13:
"of, relating to, or constituting a revival or adaptation of the classical especially in literature, music, art, or architecture"

A/AA:
"imitating or adapting the styles of the ancient classical world."

no. A is not a classical song asides from the instrumentation.
And Neo classicalism has been dead for 70 years.

Neo-classicism is no more "dead" than rhythm gaming is "dead".  Certainly, it's no longer mainstream, but a genre of music doesn't die; it just falls out of the loop.

Also, my education in folk and classical music comes from my great uncle with a Master's Degree in Education from Harvard.  According to what he has taught me and what his personal library of books and music has not only taught me but blatantly stated, classical music is a genre that is almost entirely based on instrumentation.  Classical music has no differentiation based on musical style other than "major" or "minor".  Classical songs are classified by their instrumental structure and occasionally by the nationality of the composer.  You also have the Chorale, Overture, and Opera, but those really don't tell you the style of the song; just when it would be played in a programme.