I'm not able to listen to the song at the moment, with which I can usually identify the key. Nevertheless, 95+% of the time the final chord of a song names the key -- most songs "come home" that way.
Occasionally ones runs across a song that ends on a chord other than the I (home key) chord, which tends to give "hanging in suspense" feel to it. One example is "Four Strong Winds," which ends on a V chord -- ends on D when played in the key of G. However, it does not appear that the song in question does that.
The chord sequence listed in the opening post strongly suggests to me it is indeed in the key of E. The D (bVII), G (bIII), and C (bVI) chords are not the most common in E, but they're certainly not unheard of. The equivalents in the key of C would be Bb, Eb, & Ab; in the key of G would be F, Bb, & Eb; in the key of A would be G, C, & F. There are other somewhat familiar songs that use these chords, such as "Everyday" by Buddy Holly and "To Know Him is to Love Him" by the Teddy Bears.
So yes it's a bit unusual, but it does fit in with the Cycle of Fifths and there are more songs like it.