Maintenance for the week of October 13:
• PC/Mac: No maintenance – October 13
• NA megaservers for maintenance – October 15, 4:00AM EDT (8:00 UTC) - 12:00PM EDT (16:00 UTC)
• EU megaservers for maintenance – October 15, 8:00 UTC (4:00AM EDT) - 16:00 UTC (12:00PM EDT)
• ESO Store and Account System for maintenance – October 15, 4:00AM EDT (8:00 UTC) - 12:00PM EDT (16:00 UTC)
• https://forums.elderscrollsonline.com/en/discussion/683901
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.