For this post: http://www.neo-endurance.com/off-track-skills-at-neo-petit-le-mans/ please switch to the "Text" view of the editor, paste the raw text here in the forum for us to see, and switch back to "Visual" when you're done.
What do you see when the plugin is deactivated? We ask because even without the plugin activated, WordPress has a built-in mechanism that will still turn those urls into basic embeds if pasted correctly (however, these basic embeds won't apply any customizations like the ones our plugin provides). You can learn about WordPress' basic embeds in the first paragraph of "In a Nutshell" here: http://codex.wordpress.org/Embeds
If you still don't see an embed even with the plugin deactivated, then the issue is beyond the scope of this plugin. There could be another plugin interfering. One way to troubleshoot is to deactivate your plugins 1 by 1 to see if the video appears when each plugin is deactivated.