This footage was taken at a ymca. Catch wrestling evolved from various European folk wrestling styles and was frequently performed for crowds in carnivals and circuses. The term no holds barred is referencing the catch rule set in which there was no rules. Amateur wrestling and pro wrestling evolved from Catch.
Looks surprisingly like modern high school/collegiate/Olympian wrestling.
It is an ancestor of those with the exception that they had chokes, foot locks and arm locks (what they called hooking). Two ways to win, a pin or a tap out. High school etc wrestling is very popular out in the Midwest which in my opinion is because the traveling carnivals in the 1800 - 1900 held catch events more frequently in the Midwest region it took hold there.