Hi cesgarcia
I don't see the error of loading icons when inspecting elements on your site. These menu icons belong to a custom HTML module in 'header' position so I guess the HTML tag for these icons were stripped out by default Joomla editor when you saving this custom module
You can go to Global Configuration in backend of your site > disable 'Default Editor' temporarily (set to 'None') and check the output of this module in module manager again. I put the default output of this module as our demo site here so you can compare:
<h1 data-scroll-reveal="enter top over .5s after 0s">The Best Steak House is Here</h1>
<h2 data-scroll-reveal="enter bottom over .5s after .15s">Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean semper orci semper tempus.</h2>
<a href="#restaurant" class="btn" data-scroll-reveal="enter bottom over .5s after .25s">Discover our restaurant</a>
<ul class="gk-short-menu">
<li data-scroll-reveal="enter bottom over .5s after .25s"><a href="#menu"><i class="gk-icon-dinner-set-solid"></i> <span>Menu</span></a></li>
<li data-scroll-reveal="enter bottom over .5s after .5s"><a href="#specials"><i class="gk-icon-bottle-glass-solid"></i> <span>Specials</span></a></li>
<li data-scroll-reveal="enter bottom over .5s after .75s"><a href="index.php/gallery"><i class="gk-icon-gallery-solid"></i> <span>Gallery</span></a></li>
<li data-scroll-reveal="enter bottom over .5s after 1s"><a href="index.php/reservation"><i class="gk-icon-calendar-solid"></i> <span>Reservation</span></a></li>
<li data-scroll-reveal="enter bottom over .5s after 1.25s"><a href="#location"><i class="gk-icon-map-path-solid"></i> <span>Location</span></a></li>
</ul>