Sim, ainda é necessário. Além disso, a fonte oficial do governo que você forneceu em sua pergunta, o seguinte link também deve verificar isso.
EUA Site de viagens do governo (Última atualização: 28 de janeiro de 2016)
Blood Test: All visitors and new residents to Iraq, with the exception of those travelling on a tourist visa, must have a blood test for HIV and hepatitis within 10 days of arrival or face a USD $125 fine. The test must then be repeated every 90 days while in Iraq. Guidance on where to go for the blood test is available at the airport upon arrival. In the Kurdistan Region, travelers only need to have this blood test if staying for more than 15 days.
Se eu encontrar mais alguma informação (não que você precise de mais provas), atualizarei esta resposta.
Gov.uk Site de aconselhamento de viagens estrangeiras
All visitors to Iraq, with the exception of those travelling on a tourist visa, must have a blood test for HIV and hepatitis within 10 days of arrival. The test must then be repeated every 90 days while you’re in Iraq. Guidance on where to go for the blood test is available at the airport when you arrive. In the Kurdistan Region, you only need to have this blood test if you’re staying for more than 15 days.
InterNations: Mudar-se para Erbil (parece ser um expatriado menos oficial site da comunidade)
All visitors to Kurdistan who are staying more than 15 days needs either short or long-term permissions for residency and they are required to have a blood test taken to test for HIV and hepatitis. Information on where to go to receive the test can be found on arrival at the airport.
Rekawt Hama Rasheed, the KRG Minister of Health, stated before that annually, 100,000 precautionary tests have been conducted from 2007 until 2012 while the ministry has dramatically increased this proportion to 200–300 thousand annual tests in the past three years, noting that the test is mostly done for the foreign people entering the Kurdistan Region.
Observação: Esta pergunta e resposta só se aplicam aos vistos de residência "temporários" / "de curto prazo" e "de longo prazo", não para vistos de turista.