Firstly, the Earth is a sphere, not a flat map projection like in your link. In order to fly the shortest straight distance over the curved surface of the Earth, Northern Hemisphere routes "bend" toward the poles on a flat map. The shortest routes to Central and South America from Asia or Europe often cross USA airspace or make connections in the USA.
Second, the USA is economically more influential than its mere land area indicates. There are a more big international airports located in the USA than in all of Latin America or Australia/Oceania. Flights often have connections through those USA airports instead of flying direct to smaller markets.
For example, there are exactly three flights between Asia and Latin America. A few times a week, Aeromexico flys between Mexico City and Narita, Japan (via Tiuana one way because of high/hot regulations). Similarly Emirates between Dubai and Sāo Paulo. And once a week there's an Aeromexico flight between Shanghai and Mexico City (also with high/hot limits).
Those flights can and do charge about $500-$700 extra per passenger for the luxury of avoiding the USA transit. The usual routings used by at least 10 times more passengers every day pass through US airports on those routes.
Technically it's what is called an "Geoid"[0] but for most purposes the description of an "oblate spheroid" [1] will do. Those "shortest straight distances" are called "great circles" or geodesic; an arc between two points on a spheroid also called a great distance. Technically, because the Earth isn't spheroidal but oblate, the shortest distance isn't quite a great circle. [2] The maps used for aeronautical navigation are "gnomonic" in projection to show great circles as straight lines. [3]
Second, the USA is economically more influential than its mere land area indicates. There are a more big international airports located in the USA than in all of Latin America or Australia/Oceania. Flights often have connections through those USA airports instead of flying direct to smaller markets.
For example, there are exactly three flights between Asia and Latin America. A few times a week, Aeromexico flys between Mexico City and Narita, Japan (via Tiuana one way because of high/hot regulations). Similarly Emirates between Dubai and Sāo Paulo. And once a week there's an Aeromexico flight between Shanghai and Mexico City (also with high/hot limits).
Those flights can and do charge about $500-$700 extra per passenger for the luxury of avoiding the USA transit. The usual routings used by at least 10 times more passengers every day pass through US airports on those routes.