after all seems that video autoplay block some of your template-modern javascript. i tested this code with different themes and with all works
I put in wp-content/themes/geodir_gdf-modern/header.php this
<video autoplay loop>
<source src="video-bg.webm" type="video/webm" />
<source src="video-bg.mp4" type="video/mp4" />
</video>
When i disable all javascript on your theme, then autoplay correct.
Can you check please?
url: http://rv.plusinnovative.it/
p.s. Problem is with Chrome and Safari…