An example of how you can add a 'Featured Image' column to the Event Espresso -> Events list table.

tw_ee_add_feature_image_to_events_list_table.php

<?php //Do not include the opening PHP tag if you already have one

//Add the featured image column
function tw_ee_add_event_feature_image_column( $columns, $screen ) {
    $columns = EEH_Array::insert_into_array(
        $columns,
        array( 'event_feature_image' => 'Feature Image' ), 
        'name'
    );
    return $columns;
}
add_filter( 'FHEE_manage_toplevel_page_espresso_events_columns', 'tw_ee_add_event_feature_image_column', 10, 2 );

// Display the featured image.
function tw_ee_add_event_feature_image_column_output( $event, $screen ) {
    if ( ! $event instanceof EE_Event ) {
        return '';
    }
    echo get_the_post_thumbnail( $event->ID(), 'thumbnail');
}
add_action( 'AHEE__EE_Admin_List_Table__column_event_feature_image__toplevel_page_espresso_events', 'tw_ee_add_event_feature_image_column_output', 10, 2 );

// Add CSS to the events admin for the feature image column width.
function tw_ee_custom_events_columns() {
    $css = 
        '#Extend_Events_Admin_List_Table-table-frm .column-event_feature_image {
            width: 10%;
        }';
    wp_add_inline_style('events-admin-css', $css);
}
add_action( 'admin_enqueue_scripts', 'tw_ee_custom_events_columns', 20 );