http://sridharkatakam.com/show-post-titles-category-pages-genesis/

gistfile1.php

add_action( 'pre_get_posts', 'sk_show_titles_only_category_pages' );
/**
 * Show Linked Titles Only for Posts in Category Pages
 *
 * @author Sridhar Katakam
 * @author Bill Erickson
 * @link http://www.billerickson.net/customize-the-wordpress-query/
 * @param object $query data
 *
 */
function sk_show_titles_only_category_pages( $query ) {

	if( $query->is_main_query() && $query->is_category() ) {
		$query->set( 'orderby', 'title' );
		$query->set( 'order', 'ASC' );
		// $query->set( 'posts_per_page', '2' );

		//* Remove the post info
		remove_action( 'genesis_before_post_content', 'genesis_post_info' );

		//* Remove the post thumbnail
		remove_action( 'genesis_post_content', 'genesis_do_post_image' );

		//* Remove the post
		remove_action( 'genesis_post_content', 'genesis_do_post_content' );
		remove_action( 'genesis_post_content', 'genesis_do_post_permalink' );
		remove_action( 'genesis_post_content', 'genesis_do_post_content_nav' );

		//* Remove the post meta
		remove_action( genesis_after_post_content, genesis_post_meta );
		
		remove_action( 'genesis_loop', 'genesis_do_loop' );
		add_action( 'genesis_loop', 'sk_custom_loop' );
	}

}

function sk_custom_loop() {

	global $loop_counter;

	$loop_counter = 0;

	if ( have_posts() ) : while ( have_posts() ) : the_post();

		do_action( 'genesis_before_post' );

		printf( '<div class="%s">', join( ' ', get_post_class() ) );

			do_action( 'genesis_before_post_title' );
			do_action( 'genesis_post_title' );
			do_action( 'genesis_after_post_title' );

			do_action( 'genesis_before_post_content' );
			// echo '<div class="entry-content">';
				do_action( 'genesis_post_content' );
			// echo '</div>'; //* end .entry-content
			do_action( 'genesis_after_post_content' );

		echo '</div>'; //* end .entry

		do_action( 'genesis_after_post' );
		$loop_counter++;

	endwhile; //* end of one post
		do_action( 'genesis_after_endwhile' );

	else : //* if no posts exist
		do_action( 'genesis_loop_else' );
	endif; //* end loop

}

gistfile2.php

add_action( 'pre_get_posts', 'sk_show_titles_only_category_pages' );
/**
 * Show Linked Titles Only for Posts in Category Pages
 *
 * @author Sridhar Katakam
 * @author Bill Erickson
 * @link http://www.billerickson.net/customize-the-wordpress-query/
 * @param object $query data
 *
 */
function sk_show_titles_only_category_pages( $query ) {

	if( $query->is_main_query() && $query->is_category() ) {
		$query->set( 'orderby', 'title' );
		$query->set( 'order', 'ASC' );
		// $query->set( 'posts_per_page', '2' );

		//* Remove the post info
		remove_action( 'genesis_entry_header', 'genesis_post_info', 12 );

		//* Remove the post thumbnail
		remove_action( 'genesis_entry_content', 'genesis_do_post_image', 8 );

		//* Remove the post content
		remove_action( 'genesis_entry_content', 'genesis_do_post_content' );
		remove_action( 'genesis_entry_content', 'genesis_do_post_content_nav', 12 );
		remove_action( 'genesis_entry_content', 'genesis_do_post_permalink', 14 );

		//* Remove the post meta
		remove_action( 'genesis_entry_footer', 'genesis_entry_footer_markup_open', 5 );
		remove_action( 'genesis_entry_footer', 'genesis_entry_footer_markup_close', 15 );
		remove_action( 'genesis_entry_footer', 'genesis_post_meta' );
		
		remove_action( 'genesis_loop', 'genesis_do_loop' );
		add_action( 'genesis_loop', 'sk_custom_loop' );
	}

}

function sk_custom_loop() {

	//* Use old loop hook structure if not supporting HTML5
	if ( ! genesis_html5() ) {
		genesis_legacy_loop();
		return;
	}

	if ( have_posts() ) : while ( have_posts() ) : the_post();

			do_action( 'genesis_before_entry' );

			printf( '<article %s>', genesis_attr( 'entry' ) );

				do_action( 'genesis_entry_header' );

				do_action( 'genesis_before_entry_content' );
				// printf( '<div %s>', genesis_attr( 'entry-content' ) );
					do_action( 'genesis_entry_content' );
				// echo '</div>'; //* end .entry-content
				do_action( 'genesis_after_entry_content' );

				do_action( 'genesis_entry_footer' );

			echo '</article>';

			do_action( 'genesis_after_entry' );

		endwhile; //* end of one post
		do_action( 'genesis_after_endwhile' );

	else : //* if no posts exist
		do_action( 'genesis_loop_else' );
	endif; //* end loop

}

gistfile3.css

.category .entry-title {
    font-size: 1.5rem;
}

.category .entry {
	margin-bottom: 1.5rem;
	padding-bottom: 0.75rem;
}