Maintenance for the week of April 6:
• [COMPLETE] ESO Store and Account System for maintenance – April 9, 9:00AM EDT (13:00 UTC) - 6:00PM EDT (22:00 UTC)
Play button gone from launcher after multiple kicks
Who knows? This game apart form others has legion of technical problems. But perhaps try starting it with exe file from directory? It usually works for most launcher problems.