In the shared document I can't see a matching percentage with My Phrases on the side panel.

My Phrases are linked to each user, so a user can't refer to the My Phrases of other users. 

Since the recipient user is viewing the Edit page of the shared document owner, Phrases Matches and matching percent with the My Phrases is only available for the shared document owner. 

However, since the recipient user is a different person, he can't see matching percentage with the My Phrases of the document owner.