InPrivate, Incognito, ‘Private Browsing’ is the fanciest semantic hijack of the century. It is not possible currently to run extensions only in InPrivate Browsing. Note that you can only check the box if the extension is enabled in regular mode.
Here is how you enable extensions so that they run in InPrivate Browsing mode as well: Microsoft plans to release it in March/April 2018. The feature is only available in the latest Windows 10 Insider Builds currently but will be made available to the whole Windows 10 population in the next feature updgrade. It is relatively easy to enable extensions in InPrivate Browsing mode but you can do so only on Windows 10 build 17074 or newer. Enable extensions in Microsoft Edge's InPrivate Browsing mode
