Yes, that's true, but there are a few things that are odd about the question, and even more infuriating about that "well some countries" response.
1. This is a question that is reliably google-able. From the Wikipedia page that comes up as the first result, we get.
Public Holidays in Chile:
January 1 New Year's Day Año Nuevo Blue laws forbid opening of most services.
Looking down the list for the first Chilean (e.g., *.cl) webpage, we find feriados.cl, which says:
And what does "Inalienable" mean? If one does a little bit of googling (this time in Spanish), one finds that it means basically everything shuts down, except emergency services, hotels, gas stations, and family-run businesses. But even without that knowledge, a contextual assessment (plus a working knowledge of English) will inform you that New Year's Day is a pretty big holiday in Chile.
Monday, January 1 New Year's Day
So yeah. That's easy to see.
2. The "not every country celebrates New Year's Day" is one of those facts that is true, but is useless when said out of context. What do I mean?
It is true that there are countries that don't celebrate some sort of holiday on 1 January. Strangely, a quick google search didn't pull up anything, so I ended up using the holiday information from https://www.timeanddate.com/holidays/ to build a world map that showed the countries that do and don't have some sort of national observance on 1 January:
The nine countries in red don't have any official celebrations listed for 1 January.
Note a few things:
i) All countries in South America celebrate 1 January as a holiday.
ii) All countries in the entire New World celebrate 1 January as a holidary.
iii) All countries that used to be part of the Spanish Empire celebrate 1 January as a holiday.
iv) Most of the countries that don't celebrate 1 January as a holiday are concentrated around one part of the globe.
So there is no nation in the geographic or cultural contexts in which Chile finds itself that don't celebrate 1 January as a holiday. In fact, since most countries in the entire world do celebrate 1 January as a holiday, saying "well some countries don't celebrate it" is true, but basically useless in most contexts.
In sum, we learned that Chile does have a national holiday on 1 January. The name of that national holiday - in English - is New Year's Day. And saying "well some countries don't have a holiday on 1 January" is true, but basically useless information in many contexts.
Happy New Year!