The example from the link you shared does work in IE, according to my tests. I opened the sample in a full-screen Dojo and ran it in IE 11 and it works as expected:
If you are trying to do this in an MVC app, you may need to adjust the code that locates and replaces the styles files with the new ones. The example depends on the styles files loaded one by one in the page, so if you use StyleBundles, it will not work as expected.
You can also take a look at the ThemeChooser custom widget used in the UI for ASP.NET MVC demos project. You can open the demos locally and go to Scripts/theme-chooser.js
to see the definition of the widget and then to Views/Shared/ThemeChooser.cshtml
partial view to see how the chooser is then used in a page.
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