I think the problem is in terminology. Yes, the 5th note (V) is the dominant note in name. In the key of A, and Am, the dominant note is E. Because chords are built on scale notes, and because there are different minor scales, there are also different V make ups. Using notes from natural and descending melodic minors (same scales!) E, G and B make up the dominant chord. Using harmonic and ascending melodic, the notes are E, G# and B. These are obviousle the triads. Either minor or major. The major is more pushy, and certainly gets far more use.
Now, terminology rears its head again. Getting on to the sevenths. 3 in common use. Minor seventh, major seventh and dominant seventh. Minor uses E,G,B,D. Major 7th uses E,G#,B,D#. Dominant 7th uses E,G#,B,D. Major 7th and dominant 7th both have that major sounding G#, but it's the D#/D that's crucial and confusing. Just listening will tell most people that the major 7th chord has no dominance - it's just not pushy enough.
In the song you feature, the V is E. It can just be E, it could be E7 (dom), that's up to the writer. What it won't be is Emaj7. And, theory wise, which messes up so many people, that D, which clearly doesn't belong in the key of E, is actually referenced in the key of Am, which is where the song is anyway!