There are other Arab countries. Most people know what is meant by "Saudi" even if it's technically not correct
Wikipedia: Saudis (Arabic: سعوديون Suʿūdiyyūn) or Saudi Arabians are a nation composed mainly of Arab ethnic groups who are native to the Arabian Peninsula and live in the five historical Regions: Najd, Al-Hijaz, Asir, Tihama and Al-Ahsa;