Answer: Good thing you put that "theoretically" in there at the end. Otherwise I might I thought I was being asked to write a review. But hey...
By the "riff" I think you might be referring to the recurring little bit that opens the song and is played something like this:
That's complicated by two guitars playing similar things at the same time, overlapping, one tending to arpeggiate the chords more. But the above is the basic idea.
If we knew exactly what makes a particular piece of music appealing then hit songs would be easy to produce, but I'd describe what I like about that this way: It's not the melody exactly; it's the sound: liquid, with a deep reverb and long sustain, the lead guitarist extending the life of the long notes with his tremolo bar. Two guitars of identical tone color build a seemingly intricate pattern that really is basically just two alternating chords: A minor and G. The chord progression gets more complicated than this during the vocals, but the character of the song is in that opening riff.
The long guitar improvisation later on also spends a lot of time repeating I and ii, or I, iii, ii. That contributes to a relaxed dreamy sort of feeling, because the chords don't really "go" anywhere most of the time, they don't get to the dominant V but keep repeating this inconclusive pattern.
It's kind of nice that the song begins with the impression that A minor is coming first, then G. But when it reaches the improvisation G becomes the primary chord.
Pop music makes a lot of use of "ostinato" - a constantly repeating melodic pattern (think "I can't get no satisfaction" and countless others) and also of what might be called a form of "passacaglia," a repeating harmonic pattern. In this case a really simple one during the instrumentals.
What piece of classical music does this most resemble? Well, using the term "classical" in a very broad sense, which is pretty much the way it's generally used, I'd suggest any music that rocks back and forth in a dreamy way between chords that do not include V. Portions of Eric Satie's "Gymnopedies" come to mind.
