The owner probably went into their hosting panel and edited the file names so they deleted the .htm or .html or whatever part, I guess. I have changed .htm to .html and vice versa this way so I see no reason why it couldn't be done. I might try in a bit to see. Quite why they would want to do that (other than hide that its .htm) rather than putting hyphens in the URL I really don't know as that's what's really worng with the URL! I am guessing if you then downloaded from your site onto your local machine (after deleting your original files on your PC/Mac) they would then remain that way and could be loaded up again without adding the file type again.
That would be a mod_rewrite feature that you can apply to you server for re-writing urls to be displayed as above.
this is problem of file extension, in order to do search engine friendly URL, you should put file extension at the end of URL
This is not true. You do NOT need file extensions to be "search engine friendly". In fact, a LOT of sites are going extensionless so that when they change server-side technologies, they don't have to change their URLs. With one change to their .htaccess they can invoke different server side parsers like .net or php or whatever. This site has simply gone extensionless and are hiding the trailing '/'. Have you ever looked at a WordPress site that uses SEF urls? Do you see a file extension? No... MANY content management systems are now going to extensionless URLs.