Maintenance for the week of November 3:
• NA megaservers for maintenance – November 3, 4:00AM EST (9:00 UTC) - 12:00PM EST (17:00 UTC)
• EU megaservers for maintenance – November 3, 9:00 UTC (4:00AM EST) - 17:00 UTC (12:00PM EST)
• ESO Store and Account System for maintenance – November 3, 4:00AM EST (9:00 UTC) - 12:00PM EST (17:00 UTC)
• https://forums.elderscrollsonline.com/en/discussion/684716
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.