Japan-
Shinzo Abe: 2012-current
Singapore-
Halimah Yacob: 2017-current
Lee Hsien Loong: 2004-current
South Korea-
Moon Jae-in: 2017-current
Lee Nak-yeon: 2017-current
Taiwan
Tsai_Ing-wen: 2016-current
Alternatively (with apologies for playing a bit fast and loose in terms of President/Prime Minister/Secretary - political systems come in many shapes and sizes) and note that in some of these political party doesn't make much sense - when a military strongman stages a coup and holds power for a decade and a half, is there really a ruling political party?
Japan-
Liberal Democratic Party: 1955-1993, 1994-2009, 2012 to present
Singapore-
People's Action Party: 1959 to present
Lee Kuan Yew: 1959 to 1990
Goh Chok Tong: 1990 to 2004
South Korea-
Syngman Rhee: 1948 to 1960 (interestingly, exempted himself from an eight-year limit in 1954)
Park Chung-hee: 1963 to 1979 (took power in military coup, assassinated)
Taiwan-
Chiang Kai-shek: 1950 to 1975
Kuomintang Party: 1950 to 1996, had the advantage of being a single-party state until roughly late eighties
Obviously, no: the headline is significant; east asian governments are subject to policy change and reform even within a single party rule; and this is a canard. There is a difference between indefinite rule by an abstract "party" and indefinite rule by an actual person. And China is crossing that gap.