The common reason for the issue, if you are using Crome/Other Browser instead of Internet Explorer. Browse the same URL with Internet Explorer and you can see that "Open with explorer" is enabled now.

Desktop experience feature should be activated in all servers and webclient windows service should run in all server.. Then only open in explorer View option will be enable in IE and activeX controller only works in IE not in any other browser.

If Open in Explorer option is grayed out, then its pretty sure that you are not using Microsoft Internet Explorer browser. This option only works with Internet Explorer. Note that, this option will not work in IE Edge.