Mark Takai Atomic Veterans Healthcare Parity Act of 2019 This bill includes veterans who participated in the cleanup of Enewetak Atoll in the Marshall Islands between January 1, 1977, and December 31, 1980, as radiation-exposed veterans for purposes of the Department of Veterans Affairs presumption of service-connection for specified cancers. Under a presumption of service-connection, specific diseases diagnosed in certain veterans are presumed to have been caused by the circumstances of their military service. Health care benefits and disability compensation may then be awarded.