There are alternatives to Microsoft Office, such as OfficeLibre, which is open-source and works offline, which may meet your needs.It lets you create and edit documents however, you must be online to use it and it works with documents stored on OneDrive, for which you can get a free account. There is a free version of Microsoft Office that includes Word, albeit with fewer functions.
Microsoft has become more aggressive at enforcing its licensing requirements, thus what is happening with Word 2016 on your computer. It was a trimmed-down version and is no longer distributed. Microsoft 365 plans include premium versions of these applications plus other services that are enabled over the Internet, including online storage with OneDrive and Skype minutes for home use. They’re available as a one-time purchase for use on a single PC. I do not think it shows up as unlicensed it would not give the message you are seeing. Office 2010 include applications such as Word, Excel, PowerPoint, and Outlook. There was a free version, with ads, of Office 2010 that was paid for by computer manufacturers.