Enqueue MCE Editor CSS in admin page

So I need to know the handle of CSS or a way to include that missing CSS so my content can be shown with proper formatting.

You would need to write and enqueue a new stylesheet that implements this formatting, and enqueue it on the page that requires it. You would enqueue it the same way you would for any other CSS added to WP Admin.

Note that enqueuing the TinyMCE skin file that you mentioned will not accomplish this, and will break a lot of WP Admin styling. You could copy the stylesheets content to create your own, but you would need to modify all the rules so that they are specific to your HTML markup. How you would do that is ultra specific to the HTML you’re using to display this content.