functions.php

<?php
 
/**
 * Remove Link from Title on Display Posts Shortcode
 * @author Bill Erickson
 * @link http://www.billerickson.net/code/remove-link-from-title-on-display-posts-shortcode
 *
 * @param $output string, the original markup for an individual post
 * @param $atts array, all the attributes passed to the shortcode
 * @param $image string, the image part of the output
 * @param $title string, the title part of the output
 * @param $date string, the date part of the output
 * @param $excerpt string, the excerpt part of the output
 * @param $inner_wrapper string, what html element to wrap each post in (default is li)
 * @return $output string, the modified markup for an individual post
 */
function be_display_posts_unlink_title( $output, $original_atts, $image, $title, $date, $excerpt, $inner_wrapper, $content, $class ) {
 
	// Create a new title
	$title = '<span class="title">' . get_the_title() . '</span> ';
	
	// Now let's rebuild the output
	$output = '<' . $inner_wrapper . ' class="' . implode( ' ', $class ) . '">' . $image . $title . $date . $author . $excerpt . $content . '</' . $inner_wrapper . '>';
 
	// Finally we'll return the modified output
	return $output;
}
add_filter( 'display_posts_shortcode_output', 'be_display_posts_unlink_title', 10, 9 );

Very useful Bill. thanks for this.
I've made this apply only to items which have a specific word in the post excerpt by using
if( strpos( get_the_excerpt(), 'Event' ) !== false)
but I'm stuck with making it only apply to items which are within the "Events" category.
if( strpos( get_the_category()[0], 'Event' ) !== false) crashes my page, potentially because the category list isn't passed, nor the Post ID actually, which I might have to use. Might you have any pointers?

Instead of checking the string position, you could use the WordPress function if ( has_category( 'event' ) ) { // do something }