Yes, the developer tools are installed. I wouldn't see the Office project templates in VS2015 if they weren't.
I've tried refreshing their installation, as well as uninstalling and reinstalling them. It has made no difference. The manifest is still presented as raw XML.
I've also tried this on my laptop with a clean install of Windows 10 Pro and VS2015 Community. The problem presents itself on that machine too.
Any clues or pointers would be appreciated!