Of your countries:
- Cape Verde
These are all very poor African countries. Establishing an embassy is expensive, and frankly Chilean commerce isn't so large a portion of the economy that it makes sense to do so. Now, say, China - yeah - they are investing heavily in these countries, and you want to promote trade, defense, and relations. But Chile? Not to be mean, but it's not really worth the effort. Besides - the African Union can negotiate with Chile when needed.
Gambia, for example, outsources most of its diplomatic relations to Senegal - the country that completely surrounds it. Gambia is a stretch of river smaller than Connecticut. It doesn't have the resources to maintain its own embassies.
Eriteria, as a new country (formed in 1994), is more concerned with establishing the relationships that keep it independent of Ethiopia. Chile kind of doesn't have a dog in this fight.
Niger is regularly one of the poorest countries in the world.
Of the non-African countries:
Has basically been at war for the last 10 years and is slowly rebuilding. See above.
Is an Italian protectorate. It's a small enclave the size of a single city, within Italy. It sells stamps, not diplomatic relationships.
The point of all of this is simple - diplomatic relations cost money and talent. They exist to promote peace and trade - but at a cost. For a country like the United States which has the resources, it is worthwhile (Fun fact: The United States has more people in its official military bands than in its foreign service source) but in smaller countries, you have to choose. San Marino has a population of 31,000. If they sent an ambassador to each of the approximately 200 countries around the world, that's more than 1/2 of a percent of the population. (By contrast, 1.3% of the population works for Walmart!)
tl;dr> Countries pick and choose relations based on the cost and the need.