My best friend is a historian who works with history of sports, and he always sends me sources he finds about wrestling. The article in case was published in Brazilian magazine Sport Ilustrado in 1938.
The relevant excerpt is (translation mine)
This sport was intelligently codified by Dr. B. F. Roller, former athlete and wrestler and for a long time, a medical officer in the US army, where is head of physical education.
Long studies of the secrets of the old and elegant greco-roman wrestling, of the "savatte" (mix of boxing and capoeiragem from the famous French Apaches), of the "jiu-jitsu", the famous scientific self-defense method of the nipponics, of the American "rugby", incredible for its violence and elasticity, of the Turkish fight, of the Hindu fight, and of the kilma, led to the creation of the "catch".
of the Turkish fight
Almost certainly yağlı güreş, or oil wrestling, which is a national sport in Turkey. Oil wrestling has a long history, but became differentiated from Greco-Roman wrestling without oil, so was seen as exotic in the 1930s.
of the Hindu fight
There are a number of different martial arts in the Indian subcontinent and among the wider Indian diaspora; this could refer to several forms of Indian wrestling, but probably refers to pehlwani (also known as kushti), which is one of the more prevalent grappling arts.
and of the klima
Probably glima, a form of wrestling in Scandinavia, especially Norway and Iceland.
led to the creation of the "catch".
The article is describing the system of "Catch wrestling" created by J. G. Chambers in the 1870s, which was British rather than American, and did combine a number of different international grappling styles, including pehlwani and jujitsu, and which became extremely popular in the United States, being the direct ancestor of professional wrestling. Ben Roller - the Dr. B. F. Roller of the article - was a catch wrestler in the early 1900s in the United States, where he won the American Heavyweight Championship three times, and featured in period works like Professional Wrestling (1912).