I would keep the word chain to report at the end of the game, or to compute a score.
words = [input('enter a country name: ')]
while True:
word = input('enter a country name starts with the last letter of previous country name: ')
if word and word[0].lower() == words[-1][-1].lower():
words.append(word)
else:
break
print(f"So sorry, The first letter of {word} does not match the last letter of {words[-1]}.")
print(f"Your word chain {words}")
