iCloud drive sharing on Sierra (Add People)
I was unable to find any official Apple KB article explicitly stating that High Sierra is required for sharing files with people on iCloud. I have the same OSX version and experience exactly the same problem. 

There is a workaround, however, that is officially supported by Apple - you can use iCloud.com and share files from there (PH21250). While not elegant, it certainly gets the job done. 

Performing Google query for this issue reveals that this feature is mentioned explicitly with High Sierra software (CNET or AddictiveTips). While this is not official evidence that High Sierra is explicitly required to support this feature, it may suggest that Apple is forcing users to update to the latest software to receive such feature.