The issue, according to Kevin Stadmeyer, Technical Program Manager at Google, is only relevant if the file in question was uploaded to Google Drive, was not converted to Docs, Sheets, or Slides (i.e. remained in its original format such as .pdf, .docx, etc.), the documents was made available to "Anyone with the link," and the file contained hyperlinks to third-party HTTPS websites in its content.
The flaw could allow the admins of those third-party HTTPS websites to receive header information from which the URL leading to the file could be extracted.
The issue has been solved, but previously uploaded and shared documents that meet all four of the aforementioned criteria are still vulnerable, so users are advised to create a copy of the document, share the link to it with the intended recipients, and finally delete the old file.
Last month, Dropbox has patched the exact same issue.