A family of Microsoft word processing software products for creating web, email, and print documents.
I don't have any trouble saving or opening Word or Excel files that are stored in the local Dropbox folder and subfolders on my PC, which is automatically synced with the corresponding folders on the Dropbox cloud. I can use the File > Open page, the Open dialog (Ctrl+O), or File Explorer to select or double-click the files, and the correct Office program opens them.
What is the symptom that tells you Office doesn't recognize the files? Do you see icons for a different program such as Notepad or WordPad, and does that program try to open the Office files? Or is there an error message, and if so, what is its exact text?