Possible to format droplets like all other mysite content?

I do not understand the request. How are the views droplets different so that your format cannot be applied?

I need more detail to answer.

Can you attach the format plugin file here?

I'm looking at the code and guessing that your issue is this part:

    // this is a droplet, so output the content
    else {
      $output = theme('mysite_droplet', $element['content']);
    }

The $element['content'] is already formatted by the native Views handler. I think retheming the view itself, using Views Theme Wizard, is your best approach.

Also remember that you are not required to use theme('mysite_droplet', $element['content']) here. You could use a different theme function.

The question from my end, I think, is "do you need more information about the View in order to make a theme selection?"

I get it. You would need more information about the View passed to the format layer.

The key may be in this function in droplet.inc:

function mysite_type_droplet_view_content($droplet) {
  // for blocks, the key is stored as "module|delta"
  $view = views_load_view($droplet->key);
  $output = views_build_view('embed', $view, $args, $view->use_pager, $view->nodes_per_page);
  return $output;
}

The question is: How does view_build_view() behave, and what additional arguments could you pass to it?

I have not tried the new format yet.

I am not sure either. I think it would be possible to pass a variable in the $args array in the function call:

views_build_view('embed', $view, $args, $view->use_pager, $view->nodes_per_page);

At the end of views_build_view() is the following code:

  foreach (module_implements('views_pre_view') as $module) {
    $function = $module .'_views_pre_view';
    $output .= $function($view, $items);
  }

  $view->real_url = views_get_url($view, $args);

  $view->use_pager = $use_pager;
  $view->pager_limit = $limit;

  $output .= views_theme('views_view', $view, $type, $items, $info['level'], $args);

  // Call a hook that'll let modules modify the view just after it is displayed.
  foreach (module_implements('views_post_view') as $module) {
    $function = $module .'_views_post_view';
    $output .= $function($view, $items, $output);
  }

You may be able to do what you need by implementing either a mytheme_views_pre_view($view, $items) function or a mytheme_views_post_view($view, $items, $output) function.

A small module would be required, and you would want to check the following condition:

function mytheme_views_pre_view($view, $items) { 
  if (arg(0) == 'mysite') {
   // Make your changes here.
  }
  return $view;
}

I am not certain that this will work unless the $view is passed by reference, and that does not appear to be the case.

You might also be able to override the default theme using the above conditional.

I finally looked at the new format file, and it seems to rely on other files that are not present.

Especially lines like these:

    $when_show_nodeteaser = variable_get('mysite_tools_nodeteaser', 'onmouseclick');
...
          'onclick'=>"return mysite_tools_show_nodeteaser(this, " . $element['nid'] . ");", 

Also a little change to this function in the API:

function mysite_theme_preview() {
  $name = t('Headlines list with preview');
  $output = '<div class="mysite-sample mysite-content">';
  $output .= '<ul>';
  $output .= t('<li><a href="#">Sample headline</a></li>');
  $output .= t('<li><a href="#">Sample headline</a></li>');
  $output .= t('<li><a href="#">Sample headline</a></li>');
  $output .= '</ul>';
  $output .= '</div>';
  return array('format' => $name, 'sample' => $output);
}