We know that Tom Riddle's father was a muggle. So Tom was not an Pure Blood. But in HP 2 it is said that only a true heir of Salazar Slytherin could open the Chamber of Secrets who should be a pure blood. So how could Tom open the chamber after not being a pure blood?
Because he inherited different qualities of "pure-bloods" (like speaking parsel-tongue etc.) from his maternal side i. e. Maternal grand father Marvolo and maternal uncle who themselves were the last living relatives of Salazar Slytherine himself. You can also check this video for more details: