Hi @PratikM,
Thanks for writing in.
Upon checking on your setup, the background video looping is working great. There is no delay or whatsoever. I believe the problem is the ending of the video and starting of the video. The video should not start the same as the ending part of the video so that it will not look staggered.
You could try hosting the video outside your site. for example, our demo integrity 1 video. It is hosted outside the our website. It is hosted in vimeo.
http://demo.theme.co/integrity-1/
Hope it helps. Let us know how it goes.
Thanks.