For those that are seeing the animations and don't see the setting in the main settings page, use the Settings icon by the board in Play and see if it's there.
Don't see it there either.
There was a comment here that seems to be gone now, but it helped me.
Basically, Settings - All Settings - Themes and then tick OFF Enable Special Themes. I did this and there were no animations at the start and at the finish of the game.
For those that are seeing the animations and don't see the setting in the main settings page, use the Settings icon by the board in Play and see if it's there.