You only have code with a classid for IE. Firefox ignores code with a classid.
You also specify the filename with a backslash in it (video\The Game.wmv).

Use this code for the object, that should work (filename in data and add a type that is supported by the WMP plugin):

<object data="video/The Game.wmv" style="display: inline; visibility: visible;" type="application/x-mplayer2" id="ActiveMovie1" height="315" width="442">

Honestly, I did not understand the solution that you suggested. I am not a programmer. May be the programmer that designed the website will understand your suggested solution. However, if you have a layman's solution, I'll be glad to follow that.

Which software do you use to create the page(s) and generate the HTML code?

The code that is currently generated won't work in Firefox.

You can see the current code via and search for object (Ctrl+F):

• Firefox > Web Developer > Page Source
• Tools > Web Developer > Page Source
• Right-click on a web page to open the right-click context menu and select Page Source

A good place to ask questions and advice about web development is at the mozillaZine Web Development/Standards Evangelism forum.
The helpers at that forum are more knowledgeable about web development issues.
You need to register at the mozillaZine forum site in order to post at that forum.

See http://forums.mozillazine.org/viewforum.php?f=25

I have sent the solution that you proposed to the website designer. I am still waiting for his feedback. I only paid for the website and supplied the contents.