It’s not anymore, at least not by anyone who knows what they’re talking about. It’s poorer than the US, but Mexico’s Human Development Index score is 0.756, which is officially considered “high”. But this photo of Mexico City perfectly illustrates the problem.
The problem in Mexico is inequality. The raw human development score for Mexico makes it look like Eastern Europe – not the highest, but decently good. Adjusted for inequality, however, Mexico finds itself amongst countries like Iraq and Vietnam.
So only a relatively small amount of people, limited mostly to Mexico City and other large cities, are able to enjoy very high levels of development.
Edit: Yes, technically “Third World” meant unaligned countries during the Cold War, and Finland and Switzerland were/are technically “Third World countries.” Mexico was officially one of those unaligned countries, hence its technical designation as a Third World country. But this classification was made decades ago and I answered the question as it pertains to modern usage of the term.