At first looks like the answer is hidden in the first comment in the article I linked - some filters in old IE browsers do seem to create a new z-index stacking context. I'm not at all surprised considering the amount of bugs that litter the old IE filters - from breaking of font and image alpha blending to drilling holes through iframes (this was later fixed in Windows 7 and now can be only reproduced in XP).
However there seems to be something else involved here - when you open the Menu, the dropdown is still there, just invisible (if you hover it, your pointer changes to hand). Adding position: relative to the #footer improves the things a bit - the dropdown shows but sometimes stops while animating, also the item hovers seldom work. All this seems like one of the aforementioned filter bugs in IE.
The solution I can offer you is to avoid placing anything inside a filtered element in IE. In this case, just add an element that can hold the gradient - check the updated jsFiddle
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