LiqMat: Very good points. What I was hoping to do is put a demo in Dropbox for people in a forum to download since it is not available anymore. I was wondering if that is legal.
That would definitely qualify as making copies of the work, so it would only be permitted if the rightsholder granted a license to do so (or the work is clearly in the public domain). As discussed above, some rightsholders are eager to have their work seen and shared, and will readily grant such a license with fairly generous terms (e.g. no requirement that you account how many people get copies, no payment required, etc.). Other rightsholders will, for various reasons, be picky and not grant useful licenses even when such refusal is arguably contrary to their best interest. When in doubt, get a written statement of consent from an officer of the rightsholder. Generally, that means not just some level one Customer Service Representative, but rather someone with a title that suggests they are involved in signing business relationship contracts.
You have not yet said which game or publisher is under discussion. While awaiting an answer from GOG support, you could explore the publisher's site to see if they offer a free download of the demo from their site. If they do, then instead of uploading your GOG-supplied copy of the demo, point your users to the publisher's site.