Greig was considered by many at the time to be Canada's best forward player. He was admired as a supreme ball control artist with a sudden electric shot and one of the best two-footers in the game in his day.
Greig played 19 times and captained the British Columbia All-Stars. When he was 18 he was awarded rookie honours as "Best juvenile to graduate into senior soccer". He played club soccer for Vancouver clubs Vancouver St. Andrews, and Vancouver Firefighters, and North Shore United all of the original Pacific Coast Soccer League. In his final year as a player he was named the 1963 Pacific Coast Soccer League's MVP.
He had many offers of tryouts with English clubs, but rejected in favor of remaining and playing in Canada.
In April 2002 Greig was inducted into the Canadian Soccer Hall of Fame. In 2003 at the age of 75 he died.