To convert a list field column to use a checkbox add the php excluding the first line to your theme functions.php file. The JavaScript can be placed between script tags in a HTML field on the form.

change_column_to_checkbox.php

<?php
// format: gform_column_input_content_FORMID_FIELDID_COLUMN
add_filter( 'gform_column_input_content_524_2_2', 'change_column_to_checkbox', 10, 6 );
function change_column_to_checkbox( $input, $input_info, $field, $text, $value, $form_id ) {
    $input_field_name = "input_{$field['id']}[]";
    $tabindex = GFCommon::get_tabindex();
    $new_input = "<input type='checkbox' {$tabindex} /><input type='hidden' name='{$input_field_name}' value=' ' />";
    return $new_input;
}

list_field_checkbox.js

jQuery( '.ginput_list' ).on( 'click', 'input[type=checkbox]', function() {
    elem = jQuery(this);
    elem.next('input').val(elem.is(':checked') ? 'Yes' : ' ');
}).on( 'click', '.add_list_item', function() {
    jQuery(this).parent().parent().next()
        .find('input[type=checkbox]').prop('checked', false)
        .next('input').val(' ');
});