The non-fixed type system per https://ja.wikipedia.org/wiki/%E5%92%8C%E6%99%82%E8%A8%88 was called "futei jihou" (non-fixed time system), same with other sites https://museum.seiko.co.jp/knowledge/relation_16/ . "Temporal hour system" seems like the correct translation.

My guess is that "wari koma" here means basically "separated panels" (wari: broken, koma: panel). Wadokei means (traditional) Japanese timepiece.