You should find a menu item that lets you download the file instead of playing it in your browser. Once the file is downloaded, you can double-click to get it to play in QuickTime Player.
You can also copy the URL of the link (that option should also be available in the contextual menu) and then open it directly from QuickTime Player (launch QuickTime player, choose "Open URL..." from the file menu, and paste the URL into the dialog box).