There was one player who had a difficult time getting a recent version of MacOS's Gatekeeper to allow apps from anywhere. Since changing the setting was complicated, the solution in that case was just giving them a Steam or GOG key, which got around the security problem.
If you email riotsupport@means.media we'll see if we can solve the problem. Sorry it wasn't working from the start.
Edit: We just figured out how to email purchasers, so we've emailed you to offer some help.