Ok. I was not considering the fact that the WMV video files were in a web application. For my mime setting to be applied to these files, a redeploy of the web application was required.
So, to be clear, the following is required to add a new global mime type:
1.) Add the mime type to the the domain's default-web.xml (ex. domains/domain1/config/default-web.xml)
2.) Restart the domain
3.) Redeploy the web application where the file related to the new mime type is being served.
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