Yes, it should be usable for cycling as well, and maybe other similar sports.

Check and update options on the “Run Log Options” page.

Verify the activity ID is copied fully from activity’s page address (the 10-digit number at URL’s end: connect.garmin.com/modern/activity/1004567890).
Make sure your activity is Public – activity’s privacy is set to “Everyone” (the lock icon, at the top right page corner, is open).
You may need to enable third-party cookies if currently blocked (on Google Chrome)

Endomondo service stopped on 31 December 2020.
There is no access to Endomondo website and all activities there, so you can no longer embed them.

For each activity you log, you can connect gear items (like shoes) and goals. Links to these will be displayed on the bottom of activity’s post (unless you disabled them). If you follow these links and don’t see on page top the data summery (total distance for gear, total distance+duration for goal), it might be because your site them doesn’t support archive description display (not all themes do). You can try and use a deferment theme, or if you know how to do it, you can update your them’s taxonomy.php file (if it doesn’t exist, do it to the archive.php file) by adding this line:
<?=get_the_archive_description()?>
after the title’s output.

The publication date display is theme-specific, so in some theme it will show and in others not.
If you know your way around WordPress, you can fix this relatively easy:  

1. From your browser, inspect the HTML/CSS for the publication-date in a regular post.
2. grep for a key word(s) from the above at your site’s theme files
3. In the found file(s), look for a condition excluding custom posts (e.g. by including only specific post-types).
4. Add ‘oi_run_log_post’ to the allowed post types.

Example with “Twenty Fifteen” theme:
Find this file:
wp-content/themes/twentyfifteen/inc/template-tags.php
It has a twentyfifteen_entry_meta function with this code:

if ( in_array( get_post_type(), array( 'post', 'attachment' ) ) ) {
  $time_string = '<time class="entry-date published updated" datetime="%1$s">%2$s</time>';

Add this plugin post-type like this:

if ( in_array( get_post_type(), array( 'post', 'attachment', 'oi_run_log_post' ) ) ) {
  $time_string = '<time class="entry-date published updated" datetime="%1$s">%2$s</time>';