Melody R. answered 07/31/19
Reading & Language Arts Teacher-19 years experience; remote homeschool
In the US, these are called "hand games" or "hand clapping games" (when clapping is involved. Pat--a-Cake is one well known example, though there are many more played by children). The hand slap game is often popular as is thumb wrestling. Hand clapping games are usually accompaied by a rythmic song and are part of an oral tradition. I think it may be possible to trace individal games/songs back to a specific origin, but I think it would be difficult to determine that they all originated in Korea. Though many of these games may be played in Korea, I believe they are played globally.