From 遣(や)り (yari, “doing, 連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 遣(や)る (yaru, “to do”).”) + 甲斐(かい) (kai).
やりがい • (yarigai) ←やりがひ (yarigafi)?