I’m using rtMedia and Youzer. Can Shortcodes be used to display a video gallery?

I’m not too familiar with BuddyPress and a total stranger to rtmedia. But out of curiosity I had a brief look at their documentations. Perhaps you could add a custom shortcode to your functions.php, which gets the current profile ID and uses it with the rtmedia gallery shortcode to display videos from the profile.

Something along these lines,

function my_profile_videos_shortocde( $atts ) {
  $profile_id = bp_displayed_user_id(); // not sure if this is the right function
  if ( ! $profile_id ) {
    return;
  }
  return do_shortode( '[rtmedia_gallery media_type="video" media_author="' . $profile_id . '"]' ); // add parameters to the shortcode as needed
}
add_shortcode( 'profile_videos', 'my_profile_videos_shortocde' );

You should then be able to use [profile_videos] on the Tab content field.