I have put the following short code in my post, but I get a red “x” where the button should be. I have tried different shortcodes and files with the same result.
You are seeing that red x, because download manager is not configured properly, you should see a message there, but you need to put it in wpdm settings page. However, it seems like you didn’t set any access role for the file, you can set roles from add/edit file window: