A curiously simple music effect.
Yes, I agree with you that thinking of it as a chromatic mediant gives it the most function. It should not be labeled as “Eb” but as you suggested, “D#”. In context of E major, this would then make it a non-diatonic leading tone chord, but leaving it at that overlooks the chord’s function:
The first line oscillates between “E” and “G#m”. The latter chord is a iii and is diatonic to the key. Here’s where the music gets interesting:
The 2nd line of music moves to “F#m”. In context of E major, this chord is a ii and would normally serve as a predominant. However, its predominant function is delayed by an intervening chromatic mediant (“D#”). The move between these two chords is a mirror image from the first line. It is this relationship that makes the move functionally cohesive. Add to that that this non-sequitur chord happens on the line “dreams are calling”, adding to the ethereal intent, making this chord move not only interesting but cohesive as well.