Both lost to Belgium’s Eddy Merckx, who beat Nguyen in the knockout round and Chien, Vietnam's top player, in the quarterfinal.
The Belgian made the break, a move that suits his style, against Nguyen. He led with a score 13-2 in the first three innings with two, eight and three points. Nguyen closed the gap between the sixth and 10th innings and even went into the lead (19-16).
But Merckx dominated the next seven innings scoring 31-20 to win the match 40-29.
Chien easily defeated Columbian Jose Juan Garcia in the knockout stage 40-21 to set up a clash with Merckx in the last eight.
Once again, the Belgian earned the right to break. He played error-free billiards to score 21-9 in the first half and win the match 40-28.
The 51-year-old went on to win the World Cup beating Frenchman Jérémy Bury 40-16 in the final.
Chien won €3,500 ($3,860) for his quarterfinal finish.
He and Nguyen will join Nguyen Duc Anh Chien at the World Union of Billiards World Championships to be held from November 26 to 30 in Randers City in Denmark.