Вы печатаете ввод во второе и третье предложения.Вы можете избежать этого, сделав это так:
def game():
score = 0
first_sentence = "Ala ma kota, a kot ma ... (Ale, tomka, ogon, downa): "
second_sentence = "Tylko biedronka, nie ma ... (kropek, skrzydel, ogonka): "
third_sentence = "Bez pracy nie ma ... (kolaczy, efektow, pieniedzy): "
good_answers = ['Ale', 'ogonka', 'kolaczy']
if input(first_sentence) == good_answers[0]:
second_answer = input(second_sentence)
score += 1
else:
second_answer = input(second_sentence)
if second_answer == good_answers[1]:
third_answer = input(third_sentence)
score += 1
else:
third_answer = input(third_sentence)
if third_answer == good_answers[2]:
print('Your score is:', score)
score += 1
backToGame()
else:
print('End of game.')
print('Your score is:', score)
backToGame()