Hello Nick,
you put the finger on a very interesting issue.
This slider has been created to work on Responsive templates.
Which means: it uses media queries in its CSS output.
Internet Explorer 8 and 7 cannot handle media queries (they are too old). Good responsive templates usually remedy to that problem by adding a specific javascript library such as 'css3-mediaqueries.min.js', which adds media queries functionality to IE 7 and 8.
I must admit I have forgotten to add this explanation in the documentation.
So what you need to do is add the above library (you will find it easily by just using Google search) to your template (in index.php).
Now I am thinking I should propose this advanced option in the slider module itself to take care of this issue for users who do not use the slider in a responsive template.
Once the library added, you should see some differences. But in your case, you won't be done, you will need to tweak the CSS a little for IE7 and 8, as the default right now is a clear background for the caption (IE7 and 8 also do not handle opacity correctly). You will have to make the background black since you are using caption over images that have text. But I can try and help you do that once the first issue is resolved

I am surprised, it does work for me in IE9 (IE10 in IE9 mode).

Once the media queries javascript library installed, you should not have to do anything other than adding the background color desired for the caption in the CSS file:
.caption .innercaption line 401 of style.css.php