Mark Takai Atomic Veterans Healthcare Parity Act This bill includes veterans who participated in the cleanup of Enewetak Atoll in the Marshall Islands anytime from 1977 through 1980 as radiation exposed veterans for purposes of the Department of Veterans Affairs presumption of service-connection for specified cancers. These veterans thereby become eligible for the same health care and other benefits given to service members who were involved in active nuclear tests. Under a presumption of service-connection, specific disabilities 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.