Schlegel is saying the song is in the key of A Major.

D minor in that context is a iv (minor iv chord). It would usually be IV (Major IV chord).

It's just a temporary non-diatonic chord for effect (or a temporary modulation).

A more annoying term to use here would be Modal Interchange, which means you're using a chord from a different mode -- in this case a closely related key. A minor is closely related to A major. With just a single note changed in that D chord (F# changed to F natural) you get an interesting effect, in this case that "melancholy" thing. It's "wrong" but in a good way, because it's just a single note difference.

One chord (one note) is a small enough difference that it doesn't totally disrupt the tonality of the overall piece. It's just a momentary chord that strikes our ear for effect.

-Carl.