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The questions seem not clear. Thus, this is how I understood the questions:
Question 1: Which countries have 2 days of holiday for New Year ->> This question asks about which countries have 2 days of New Year and those 2 days are public holidays. Based on the result, there are 20 countries with 2 days of New Year which are at the same time Holiday.
Question2: What are the countries that don't have New Year's day as a Holiday? ->> This question asks about which countries have indeed New Year's day but don't recognize it as a public holiday. Based on the result, there is only one country with New Year's day but don't recognize it as a Holiday.