Are you perhaps able to look st the preference in settings - display - full screen apps.
Current Phone ~
Samsung Note 20 Ultra 5G SM-9820 _ Samsung One Ui 2.5/ Android 10. Snapdragon 865+
Welcome to the Community! :smileyhappy:
seems the only way to exit some games is as you say tap at the bottom of the screen which is not easy and also the game is still open and the only way of closing the game is to close the app button. There is no setting the game to exit and this is also true of other games.