Something is wrong with the map. From Mexico to Chile, except Brazil and very few other countries, they were colonies of Spain.
Discussion
The most important colonies were Mexico, Peru and La Plata (Argentina and part of Bolivia), and they were called viceroyalties.
The presence of the British Empire was thanks to piracy, mainly along the entire Pacific coast.
It's not very accurate, and oversimplified but here is some more explanation for this map
https://www.statista.com/chart/amp/3441/countries-never-invaded-by-britain/
According to the book "All the Countries We’ve Ever Invaded: And the Few We Never Got Round To," there are only **22 countries** that Britain never invaded throughout history. These countries managed to avoid British invasions:
1. Andorra
2. Belarus
3. Bolivia
4. Burundi
5. Central African Republic
6. Chad
7. Congo
8. Guatemala
9. Ivory Coast
10. Kyrgyzstan
11. Liechtenstein
12. Luxembourg
13. Mali
14. Marshall Islands
15. Monaco
16. Mongolia
17. Paraguay
18. Sao Tome and Principe
19. Sweden
20. Tajikistan
21. Uzbekistan
22. Vatican City ¹²
It's fascinating to see how Britain's warfaring efforts touched nearly every corner of the globe, but these few countries remained untouched by British invasions.
Source: Conversation with Bing, 03/03/2024
(1) Only 22 countries have never been invaded by Britain - Statista. https://www.statista.com/chart/3441/countries-never-invaded-by-britain/.
(2) Map of the Week: Every Country Britain HAS NOT Invaded. https://blog.richmond.edu/livesofmaps/2023/10/13/map-of-the-week-every-country-britain-has-not-invaded/.
(3) Luxembourg one of only 22 countries never invaded by Britain - RTL. https://today.rtl.lu/news/luxembourg/a/1422840.html.
(4) Countries of the world that Britain has not invaded or occupied. https://vividmaps.com/britain-empire/.
(5) Which Countries Were Never Invaded By Britain? - WorldAtlas. https://www.worldatlas.com/articles/which-countries-were-never-invaded-by-britain.html.
(6) undefined. 
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(7) undefined. https://www.statista.com/chartoftheday/.