First of all, I don't hear it as "I love her, I love her...". It's just vocalisation, "la da da, la da da"... That seems pretty important.
It's exactly like you said, he looks at this relationship and wonders what they see in each other, while he's feeling left out ("cheat the life out of me, as you walk hand in hand..." is a very dramatic way of saying that). And he ends up wishing for the demise of their relationship. How mean
. It's the antithesis of Happy Lovers At Last United.
It is kind of similar to Driving Your Girlfriend Home except that here it's the girlfriend herself asking "What do I see in him?".