Burgin was the author of the memoir Islands of the Damned: A Marine at War in the Pacific (with William Marvel). Burgin is portrayed in the HBO miniseries The Pacific by Martin McCann. Burgin himself appears in documentary footage during the miniseries.

Burgin joined the United States Marine Corps on November 13, 1942, during World War II and was assigned to the 9th Replacement Battalion. He soon became a mortarman in K-Company, 3rd Battalion, 5th Marines, 1st Marine Division (K/3/5), and fought in the Pacific War at Cape Gloucester, then alongside his friends Eugene Sledge and Merriell "Snafu" Shelton, on Peleliu, and Okinawa. Burgin was promoted to the rank of sergeant upon reaching Okinawa.

He was awarded a Bronze Star for his actions in the Battle of Okinawa on 2 May 1945, when he destroyed a Japanese machine gun emplacement that had his company pinned down. He also was to be recommended for a Silver Star by Captain Andrew "Ack-Ack" Haldane for destroying a pillbox on Peleliu, but Haldane was killed by sniper fire before he could submit the recommendation.