This is the intro to the video:
"The one thing all humans have in common is that each of us wants to be happy, says Brother David Steindl-Rast, a monk and interfaith scholar. And happiness, he suggests, is born from gratitude. An inspiring lesson in slowing down, looking where you’re going, and above all, being grateful."
Let me persuade you. Monotheism capitalizes on the fact that gratitude is happiness. When a person considers everything around them to be the will of a loving God, there is essentially nothing they can't be grateful for. No other persuasion offers more gratitude and a return of happiness than monotheism.
You mention the loving characteristic of God. With monotheism everything is the will of God and there is nothing one could point to and say "that's not from God". And so the demonstration of God's love is his will to create love in people. This is why some people believe Jesus is God, because he was a creation full of love and kindness.
It is important to note that the speaker in the video merely makes an observation and that means it is not scientific. However, I am confident that if someone really took monotheism to heart and started to praise God throughout the day, and they did this habitually, they would feel happier than before they started out.