Once you have pushed all the markers within the array using the loadMarkers method, ensure that you call the MarkerCluster api. Remember to include MasterCluster.addMarkers(markers) after the jquery.each loop.

Furthermore, make sure to save the reference of the MasterCluster instance on line 99 in app.js and pass it to the loadMarker method. This will allow you to call the addMarkers api on it.

For optimal performance, it is recommended to declare and initialize the markerCluster after loading the markers

var markerCluster = new MarkerClusterer(map, markers,{
  imagePath: 'https://example.com/markerclusterer/m',
  zoomOnClick: true
});

Once the initialization process is completed at line 100, save the MarkerCluster instance in a variable like so:

var cluster = new MarkerCluster(map);

When invoking loadMarkers() in the next line, pass this variable as shown below:

loadMarkers(cluster);

Receive the argument in the loadMarkers function as demonstrated below:

function loadMarkers(markerCluster) { // markerCluster will be utilized in the final line of this function as depicted below.

Within the loadMarkers function, following the jQuery foreach loop, insert the following line:

markerCluster.addMarkers(markers);

Your code is in need of some adjustments. The recommendations I provided were not followed. If you haven't made any other changes, simply replace your entire app.js file with the code below. I have made the necessary modifications and included the complete file.

var map;
var markers = [];

/* MAP FILTER */

// Capture click on the input
jQuery(function () {
    jQuery('input[name=filter]').change(function () {
      var filterClickId = jQuery(this).attr('id');
      MarkersFilter(filterClickId);
  });
});

// Show or hide marker based on the input state
function MarkersFilter(category){
   if (document.getElementById(category).checked===false) { // Hide the marker
      for (var i=0;i<markers.length;i++) {
         if (markers[i].properties==category)  {
            markers[i].setVisible(false);
         }
      }
   } else { // Show the marker
      for (var i=0;i<markers.length;i++) {
         if (markers[i].properties==category)  {
            markers[i].setVisible(true);
         }
      }
   }
}

/* END MAP FILTER */

/* ICONS FOR DIFFERENT TYPES */

var iconBase = '/mapshapes/';
        var icons = {
          schools: {
            icon :{
              url: iconBase + 'schools_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          trade: {
            icon: {
              url: iconBase + 'trade_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          culture: {
            icon:{
              url: iconBase + 'culture_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          health: {
            icon:{
              url : iconBase + 'health_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          sports: {
            icon:{
              url: iconBase + 'sports_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          safety: {
            icon:{
              url: iconBase + 'safety_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          catering: {
            icon:{
              url: iconBase + 'catering_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          publictransport: {
            icon:{
              url: iconBase + 'publictransport_maps.svg',
              scaledSize: new google.maps.Size(35, 35),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          },
          libris: {
            icon:{
              url: iconBase + 'libris.png',
              scaledSize: new google.maps.Size(70, 70),
              origin: new google.maps.Point(0,0),
              anchor: new google.maps.Point(0, 0)
            }
          }
        };

function loadMarkers(map) {

  var infoWindow = new google.maps.InfoWindow();
  geojson_url = '/project.geojson';

  jQuery.getJSON(geojson_url, function(result) {
      data = result['locations'];
      jQuery.each(data, function(key, val) {
        var point = new google.maps.LatLng(parseFloat(val['geometry']['coordinates'][0]), parseFloat(val['geometry']['coordinates'][1]));
        var titleText = val['properties']['name'];    
        var address = val['geometry']['address'];
        var marker = new google.maps.Marker({
           position: point,
           title: titleText,
           icon: icons[val['type']].icon,
           map: map,
           properties: val['type']
        });
        mc.addMarkers(markers);
        var markerInfo = "<div><h3>" + titleText + "</h3> " + address + "</div>";
        marker.addListener('click', function() {
          infoWindow.close();
          infoWindow.setContent(markerInfo);
          infoWindow.open(map, marker);
        });
        markers.push(marker);
      });
      var Marker = new MarkerCluster(map, markers, {imagePath: 'http://localhost/libris/mapshapes/'});
  });
}

/* CREATE MAP */
function initMap() {
    map_options = {
      zoom: 16,
      center: {lat: 50.808757, lng: 4.314472},
      styles: [
    {
        "featureType": "administrative",
        "elementType": "labels.text.fill",
        "stylers": [
            {
                "color": "#444444"
            }
        ]
    },
    {
        "featureType": "landscape",
        "elementType": "all",
        "stylers": [
            {
                "color": "#f2f2f2"
            }
        ]
    },
    {
        "featureType": "poi",
        "elementType": "all",
        "stylers": [
            {
                "visibility": "off"
            }
        ]
    },
    {
        "featureType": "road",
        "elementType": "all",
        "stylers": [
            {
                "saturation": -100
            },
            {
                "lightness": 45
            }
        ]
    },
    {
        "featureType": "road.highway",
        "elementType": "all",
        "stylers": [
            {
                "visibility": "simplified"
            }
        ]
    },
    {
        "featureType": "road.arterial",
        "elementType": "labels.icon",
        "stylers": [
            {
                "visibility": "off"
            }
        ]
    },
    {
        "featureType": "transit",
        "elementType": "all",
        "stylers": [
            {
                "visibility": "off"
            }
        ]
    },
    {
        "featureType": "water",
        "elementType": "all",
        "stylers": [
            {
                "color": "#46bcec"
            },
            {
                "visibility": "on"
            }
        ]
    }
]
    }


    map_document = document.getElementById('projectmap');
    map = new google.maps.Map(map_document,map_options);
    loadMarkers(map);
}

google.maps.event.addDomListener(window, 'load', initMap);