Found a post where a ZOS member replies and gives some steps to try to fix it, but the player who responded at the bottom says he had the same issue and describes how he fixed it.

I'd recommend trying out the solutions ZOS recommended first, and the player's personal fix at your own discretion.

Here is the thread: https://forums.elderscrollsonline.com/en/discussion/431990/launcher-doesnt-launch-game-after-i-press-play