For those issues, I would use a proxy website to work around the security. I ran one in high school to access things I shouldn't. The problem with the launcher in your case is the fact that every time it updates, which is daily, it has to access the same website from which you downloaded the launcher from. What confuses me is why GitHub is blocked on your security, and not manofteals website. Both websites are verified and secure. (Hence the https instead of http). I could provide you a link, but the moment you run it, it will fail since GitHub is blocked. I would use the traditional manual downloading and create a shortcut on your desktop with a link directly to OpenRCT2's website.

Hope that helps!