Sorry. Think you misunderstood the post you are referring to and the embed feature in general.
Basically the embed feature only works with certain video/image providers that use an "oEmbed" protocol like youtube, dailymotion, vimeo (mentioned in the post), flickr and a few others. There is a list of providers someplace (I don't have) but you could try google for it. Does not have to be a WP list. Be aware any list is never complete.
If the link you enter does not support the oEmbed protocol then WP will only give a link, which is what you are getting.
Am not an expert but used the protocol for an application I wrote. The link like the standard youtube.com link is able through the protocol to then return info in text format for height, width, url (for the content), format and other things. That stuff is used to be able to play the video or show the image.
Hope that helps. But to do what you want you will need a plugin of which there are several.