Maintenance for the week of April 6:
• [COMPLETE] ESO Store and Account System for maintenance – April 8, 9:00AM EDT (13:00 UTC) - 6:00PM EDT (22:00 UTC)
Don't click install. Wait. They know it's an issue, and they're resolving it.
Edit: If you're an idiot like me and clicked "Install" because you like shiny buttons, cancel the update and repair the launcher. That appeared to work for me.