We are already using Gitlab in our development process. We want to integrate our specification files (which currently are Word documents) into our repository, in order to leverage the versioning of Git. Our stakeholders are not engineers, so my quesiton is: how could we use that setup to let them modify easily the specifications and store them in Gitlab? And more broadly, if you have done something like that, I'm interested in your feedback.
You won't be able to use Word documents effectively within a git repository. You could use your repo to check in the Word document file and version it, but you wouldn't be able to do diffs or handle merge conflicts. It could even add overhead to the team, depending on who has the right access permissions and knowledge to be able to use git to control the version.
If you want to use GitLab features, GitLab has a wiki, a static site editor, and issues that are more friendly for stakeholders, but they would need some level of access to GitLab. If you want to continue using a Word document, you may want to look at document management tools that are designed to work with Word documents (which would also likely work with other Microsoft Office formats, like Excel and PowerPoint).