Hi,
thanks for your post, and sorry for the trouble.
The reason for this is that the WP YouTube player plugin does not use regular WordPress Shortcodes, but its own custom implementation. Those do then not work in tables, out of the box.
We could make them work with a single extra line of code, but I’d actually propose a different way:
The new WordPress 3.6 has support for embedding videos built-in. So, I suggest that you update to WordPress 3.6, deactivate/uninstall the WP YouTube Player plugin and change the Shortcode to
[embed]https://www.youtube.com/watch?v=pabGBl72zPI&feature=youtu.be&autoplay=1[/embed]
That will also embed the video nicely.
(If you’d rather keep using WP YouTube Player, just let me know, and I’ll find the necessary code.)
Regards,
Tobias