Links to other Office programs use OLE (Object Linking and Embedding). OLE links are always absolute, never relative.
To relink to the spreadsheet in the same folder, choose File>Info>Edit Links to Files. Select a link and choose Change Source. Then select the spreadsheet in the same folder as the Word file.
Long ago (20-25 years, approximately), it was possible to edit link field text directly in the Word document, and temporary relative fields could be created. But that process was just as tedious and repetitive and considerably more error-prone than the current routine.