I had to run it from an elevated command prompt and it did the job beautifully. After a bit more Google-fu I came across this page, where the author was sharing a VBScript received from Microsoft support rep that manually removes Office 2010 (2007 version is also available). There seem to have been some tools available on Microsoft support sites, but they were all now linking to non existing pages. I started looking into ways to force-remove MS Office 2010. Because of the slowness of the PC in question, every attempt to uninstall and then roll back the changes was taking at least 30 minutes so it wasn't a practical solution. Every time it would go a bit further and fail on different registry keys. Initially, I tried to resolve the issue by fixing permissions for the offending registry keys and re-running the uninstaller.

Normal uninstall fails with error 1402 (in French) about permission issues on some registry entries. Office 2010 is interfering with some Outlook 365 plugins that user requires so needs to be removed.

A very old and slow HP Windows 7 laptop with MS Office 365 and MS Office 2010 installed.

Office 2010 removal tool