I believe this a kind of word-game, but cannot find a reference to it...
ひとこと欄 is not the name of a game. It means “a place for a short message.” It is often found at the end of various forms. For example, an application form of a fitness center may have ひとこと欄 at the end with a sentence such as “If you have any suggestions or concerns, please write them here.”
I do not know its English equivalent, but I post this as an answer because japanese.stackexchange.com is a website for questions about Japanese, not for questions about English.