A simple custom template that has a background video. It is based off the Wide default template.

awe_video.php

<?php $weather_name = awesome_weather_preset_condition_names_openweathermaps( $weather->data['current']['condition_code']); ?>

<style>
	.awesome-weather-main-content {
		position: relative;
		z-index: 10;
	}
	.awesome-weather-video-background {
		position: absolute;
		top: 0; right: 0; bottom: 0; left: 0;
		overflow:hidden;
		z-index: 0;
	}
	.awesome-weather-video-background video {
	    position: absolute;
	    min-width: 100%;
	    min-height: 100%;
	    max-width: none;
	    max-height: none;
	    top: 50%;
	    left: 50%;
	    -webkit-transform: translate(-50%, -50%);
	    -ms-transform: translate(-50%, -50%);
	    transform: translate(-50%, -50%);
    }
</style>

<div id="awesome-weather-<?php echo $weather->city_slug; ?>" class="awe_wide awe_video <?php echo $background_classes ?>" <?php echo $inline_style; ?>>

	<div class="awesome-weather-video-background">
	<video loop="" muted="" autoplay="" poster="<?php echo $weather->background_image; ?>">
            <source src="http://urltovideo/<?php echo $weather_name; ?>.mp4" type="video/mp4">
            <source src="http://urltovideo/<?php echo $weather_name; ?>.webm" type="video/webm">
	</video>
	</div>

	<div class="awesome-weather-main-content">
	  
	  <?php awe_change_weather_form( $weather ); ?>
	  
		<div class="awesome-weather-header awecf"><span><?php echo $header_title; ?><?php awe_change_weather_trigger( $weather ); ?></span></div>
	
		<?php if( isset($weather->data['current'])) { ?>
		
			<div class="awecf">
			<div class="awesome-weather-current-temp">
				<strong>
				<?php echo $weather->data['current']['temp']; ?><sup>&deg;</sup>
				<?php if($weather->show_icons) { ?><i class="<?php echo $weather->data['current']['icon']; ?>"></i><?php } ?>
				</strong>
			</div><!-- /.awesome-weather-current-temp -->
			
			<?php if($weather->show_stats) { ?>
			<div class="awesome-weather-todays-stats">
				<div class="awe_desc"><?php echo $weather->data['current']['description']; ?></div>
				<div class="awe_humidty"><?php echo $weather->data['current']['humidity']; ?>% <?php _e('humidity', 'awesome-weather-pro'); ?></div>
				<div class="awe_wind"><?php _e('wind:', 'awesome-weather-pro'); ?> <?php echo $weather->data['current']['wind_speed']; ?><?php echo $weather->data['current']['wind_speed_text']; ?> <?php echo $weather->data['current']['wind_direction']; ?></div>
				<div class="awe_highlow"><?php _e('H', 'awesome-weather-pro'); ?> <?php echo $weather->data['current']['high']; ?> &bull; <?php _e('L', 'awesome-weather-pro'); ?> <?php echo $weather->data['current']['low']; ?></div>	
			</div><!-- /.awesome-weather-todays-stats -->
			<?php } ?>
			</div>
			
		<?php } ?>
		
		<?php if($weather->forecast_days != "hide") { ?>
		
			<div class="awesome-weather-forecast awe_days_<?php echo count($weather_forecast); ?> awecf">
		
				<?php foreach( $weather_forecast as $forecast ) { ?>
					<div class="awesome-weather-forecast-day">
						<?php if($weather->show_icons) { ?><i class="<?php echo $forecast->icon; ?>"></i><?php } ?>
						<div class="awesome-weather-forecast-day-temp"><?php echo $forecast->temp; ?><sup>&deg;</sup></div>
						<div class="awesome-weather-forecast-day-abbr"><?php echo $forecast->day_of_week; ?></div>
					</div>
				<?php } ?>
		
			</div><!-- /.awesome-weather-forecast -->
		
		<?php } ?>
		
		<?php awe_extended_link( $weather ); ?>
		
		<?php awe_attribution( $weather ); ?>
	</div>

</div><!-- /.awesome-weather-wrap: video -->

You would need to change the function at the very top to: awesome_weather_preset_condition_names_yahoo