I am using joomla 2.5.10

Finally, navigate to Extensions >> Plugin Manager (all Joomla! versions) and publish the plugin. To edit the plugin parameters, simply click on its name "AllVideos (by JoomlaWorks)".

I can't click on it in manage extensions.
I see the tooltip come up ... that's it.

Please
-upgrade to Joomla 2.5.11
-install Admin Tools from www.akeebabackup.com/ in order to fix your permissions as they should be

and
- then reinstall the extension.

Right permissions on all joomla sites:
755 for folders
644 for files