See: Conan Exiles Dedicated Server Launcher (Official Version: 1.3.8 / Beta: 1.4.0) - #1959 by Toolguy
If you want an older version, you need to copy the link and use something like Internet Explorer, or any other browser that does not try to use HTTPS everywhere, because for some reason the place where the files are hosted is failing at answering HTTPS requests (works in HTTP).