battledore; hagoita
An old or dialectal term for a 羽子板 (hagoita), a wooden paddle used in the traditional game of hanetsuki. Rare in modern standard Japanese; 羽子板 is the common word.
See also: 羽子板
In some regions, a hagoita is called 'kogiita'.
The exact origin is uncertain. The kanji 胡鬼板 are likely ateji for the reading こぎいた, possibly related to 羽子板 (hagoita).