I've inserted SWF file into the course homepage by using the embed media tool but the SWF is not played.
In fact solution affects all file types not only swf.
To make file automatically open ("without downloading", in fact file is downloaded and is opened from user's temp folder) you need to set permissive permission Level for Browser File handling.
Go to Central Administration > Manage Web Applications > [Highlight a web application] > click General Settings in the Ribbon > Scroll down in the General Settings window to see Browser File Handling. Set as desired. Save settings.
See image attached.
Browser File Handling was introduced into SharePoint 2010 as a security feature and the same applies to SharePoint 2013. When a user requests a file within SharePoint, the web server (IIS) will respond including the “X-Download-Options: noopen” HTTP Response Header if Browser File Handling is set to Strict and the file (MIME) type accessed is not on the Web Applications trusted file (MIME) type list. This header works in conjunction with Internet Explorer (version 8 or higher) to prevent potential security risks when accessing files online and will stop files from being directly opened.
There are two options for Browser File Handling – “Strict” and “Permissive”.
“Strict” specifies the MIME types which are not listed in a Web Application’s AllowedInlineDownloadedMimeTypes property (more on this in a bit) are forced to be downloaded.
“Permissive” specifies that the HTML and other content types which might contain script are allowed to be displayed directly in the browser. In other words, no matter what the type of content, if it lives within SharePoint, the file will open in your browser.