A .swf file will play in the Flash Player... by itself only on machine that have the Flash program installed... which you do it sounds like.... otherwise the .swf will open in a Web browser which has the Flash pluggin installed.
So what seems to be happening is that
1. The Flash .swf is not finding the Flash program
2. the .swf does not have the Flash program as it's "file association" or program used to open these type of files. This can be set to whatever program by the way. For example, you could associate MSWord with .swf files ... result.. won't open in Word so opens in Browser instead.

To change/check file association,
http://windows.microsoft.com/en-US/w...ses-by-default
Best of luck!
VM