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On your site, this CSS rule is preventing box-shadow from working in IE9:

table, table td 
 border-collapse: collapse;

See: box-shadow on IE9 doesn't render using correct CSS, works on Firefox, Chrome

You must add border-collapse: separate; to the element that box-shadow
is not working on.

So, this should fix the problem for you:

.fancy 
 border-collapse: separate;

box-shadow is supported from IE9 onwards.

There are plenty of sites out there describing how to do this for older IEs. One of them is: http://www.useragentman.com/blog/2011/08/24/how-to-simulate-css3-box-shadow-in-ie7-8-without-javascript/

Also check out: http://www.css3.info/preview/box-shadow/

My personal opinion in general on making older browsers do things they actually cannot is this:
Avoid it. Instead apply the principles of progressive enhancement. Also explain to your client that solving problems of outdated, non standard browsers with non standard solution, is very time consuming and probably not worth the effort.

It works fine in IE 9.

Earlier versions doesn't support box-shadow, but you can use a filter:

zoom: 1;
filter:
 progid:DXImageTransform.Microsoft.Shadow(Color=#eeeeee, Strength=15, Direction=90),
 progid:DXImageTransform.Microsoft.Shadow(Color=#eeeeee, Strength=15, Direction=180);

Read: http://www.useragentman.com/blog/2011/08/24/how-to-simulate-css3-box-shadow-in-ie7-8-without-javascript/

You could also use http://css3pie.com/

PIE makes Internet Explorer 6-9 capable of rendering several of the
most useful CSS3 decoration features.

From google: filter: progid:DXImageTransform.Microsoft.Shadow(color='#cccccc', Direction=135, Strength=3);

Probably not exactly as you want it, but fiddle around with it or look into DXImageTransform some more.

On IE you need to use filter for that effect.

filter:progid:DXImageTransform.Microsoft.Blur(PixelRadius=3,MakeShadow=true,ShadowOpacity=0.30);
-ms-filter: "progid:DXImageTransform.Microsoft.Blur(PixelRadius=3,MakeShadow=true,ShadowOpacity=0.30)";
zoom: 1;

By default IE was setting up IE10 Compatibility mode which should be replaced with IE 9 using meta-tag. So, whenever it will be running on other browsers then it will use the CSS that will be compatible with IE9. As in IE10 Compatibility mode box-shadow CSS property has been removed from the library

We can use meta-tag in head just to change the document compatibility level:

<meta http-equiv="X-UA-Compatible" content="IE=8,IE=9" />

Above tag is showing that make this document compatible with IE8 and IE9 for browsers other than IE8 and IE9 switch CSS level to IE9.

I believe this issue is specific to your browser, because it works for me in this jsFiddle on both IE9 & Chrome. The link you provided works in Chrome, but not in IE9. This would indicate that the issue is specific to your implementation.

I would check to make sure that compatibility mode is disabled, and also make sure you don't have any settings enabled that would interfere with CSS. I would also suggest testing this in multiple browsers and using process of elimination to determine why it isn't working.

EDIT

I was just looking at your markup. Try removing this line and see if it makes a difference:

<meta http-equiv="X-UA-Compatible" content="IE=edge" />

It's already 2018, happens the same with IE11.
Sometimes the box-shadow doesn't work, but sometimes it does.

I tried this with IE11 and IE10:
Try changing the display of the element where you want to add the shadow (usually "display: block" works fine):

.fancy 
 display: block;
 border: 1px solid black;
 margin: 10px;
 box-shadow: 5px 5px 5px #ccc;