Our joint work on identifying the name of this game has yielded amazing results. See for yourself below!

Thanks to everyone who sent information and got involved in the joint action.

Poland: Latawiec
México (en lenguaje purépecha): Kansakata
México: Papalote (en idioma mexicano náhuatl)
Pakistan: Patang, Patang Bazi (in Urdu) and Guddi uraan (in Punjabi)
Spain (en castellano): Cometa, volar cometas
Spain (Murcia): Birlocha
Spain (Valencia): Cachirulo
Spain (Catalan): Milotxa
Maroc: Tayyara (en árabe الطيارة
Croatia: zmajevi, puštati zmajeve
Serbia: puštati zmajeve u vazduh, zmajevi
Tunisia: Afrit
Brasil: Arraia, Papagaio, Pipa
Argentina: pandorga, barrilete, cometa
Germany: Drachenfliegen or Drachen steigen lassen
France : jeu de cerf-volant
Afghanistan : gudiparaan baazi (But it's rather a "fight" as you fly your kite to slice the strings of the other kites.) The smaller kites for children are called "patingak" - small butterfly - or "mahibak" - small fish. The talibans have prohibited kite flying.
Vietnam : Diều
Cuba : el papalote (There are four kinds of different kites: hiringas, cometas, papalotes and coroneles.)
Japan : tako, edo (rectangular kites) and rokkaku, the last ones being used in "fights". There are also kites for celebrating (hamamatsu, O-Dako for example).
India : patang (but there are mainly used for "fights" as in Afghanistan. The cutting string is called "manjha". There are two main festivals in Jodhpur and Ahmedabad.)
Korea : yeon and bangpae yeon. They have no tail. They can be used in "fights" too.
Indonesia : layang-layang (kites for "fights") and kaghati which are made out of cassava leaves and pineapples fibers.
Malaysia : wau, with three main different kinds: wau bulan (moon kite), wau kuching (cat kite) and wau jalabudi (woman kite).
Thailand : chula and pakpao, which are "male" and "female" kites used in "fights". There has been a competition called the Royal Cup since 1903.
Cambodia : klèng
Honduras : el papalote
Chile : volantin
Guatemala and Argentina : barilete
Nicaragua : papagayo
Ecuador, Colombia, Panama, Peru, Uruguay : comete
Brazil : pipas, which is a "fight" kite
Nepal : malay, which are diamond-shaped.
Italy: aquilone
Portugal: Estrela-star, papagaio-parrot.