The video background is still not fitting the mobile screen as you can see in the image attached.

I can see it is fitting well in your shared screenshot. If you are referring its height then it can’t fit on mobile as there is constraint due to video aspect ratio.

If not possible to have 100% fitted, how can I put an image background for mobile and a video background for laptop?

You can achieve this using following custom CSS code.

@media (max-width: 800px) {
#home #VideoWorker-0 {
    display:none;
}
.sh-section-accc22f04d32fce11ef4dfe63fa6bf51 {
    background-image: url(//www.3dtour.pt/wp-content/uploads/2017/05/Wallpaper.png) !important;
    background-position: 0 0;
}
}