I keep getting this message while trying to launch the patcher, "We are unable open your game client. Please restart your computer and try again. If the same error occurs, please delete all previous MapleStory game files and re-install the game client from maplestory.nexon.net." I've redownloaded the installer several times and have restarted my computer several times as well. Am I supposed to download the official game then move all the Royals files over to that folder?
No, you just need the the files from the download page here. Do you perhaps have other maple versions installed? Because I haven't heard anyone here get that nexon message before. Otherwise you can try the things in this guide.
Then your AV is deleting it. Disable your AV, download and install, then add Royals.exe to the exceptions list, and finally enable your AV again.