In 2007, he won the African Individual Chess Championship in Windhoek, Namibia, earning a spot in the 2007 Chess World Cup. In this qualification tournament for the 2010 Chess World Championship Gwaze was eliminated in the first round by fifth-seed Alexei Shirov. In 2010 he came first in the Cuca Trophy international tournament in Luanda, Angola. He took part in the Chess World Cup 2011, but was eliminated in the first round by former FIDE World Champion Ruslan Ponomariov.