Not sure if this is the right place to ask, but why does 子捕り mean (a game of) catch-the-child? What part of the reading makes it a game? What kind of game is "catch-the-child"? I'm just desperately curious for the context.
If you click on each kanji of the word, you'll see in the dictionary that 子 is child and 捕 means catch. The り at the end kind of turns it into a noun (I'm not good with grammar terms).
I would say, literally the word just means "child-catching", but the word is most commonly used for that game. There are different Japanese words for kidnapping, so there is little to no chance of misunderstanding this in other ways (at least for Japanese people).
I guess it's like "baseball" usually refers to the sport and there is no need to say "baseball sport".