Games was largely self-taught as a designer, leaving St Martin's School of Art after just two terms in 1930. Yet in 1930s Britain, he still managed to slowly establish himself as a freelance poster designer.
He joined the infantry as a private in 1940, but was called upon to design a recruiting poster for the Royal Armoured Corps in 1941 by the War Office. Appointed official war poster designer (1942–6) with Frank Newbould as his assistant, several of his designs attracted controversy, notably the ATS 'glamour girl' of 1941 and the “Talk in Here” poster of 1944 - the first two of which were withdrawn.
Games had a personal philosophy of 'maximum meaning, minimum means', which applied to his posters too. Whenever creating a new design, Games would deliberately work on a small scale, since he believed that posters had to be effective from a distance.
As an Official War Artist during World War II, he designed over a hundred posters and later produced the commemorative stamps for the 1948 Olympic Games (earning himself the nickname ‘Olympic Games'). He also secured the projects to create the symbol of the Festival of Britain in 1951, which became one of the most popular images of post-war Britain, and in 1955 BBC Television's logo. In 1958 Games was awarded the OBE for services to graphic design.
Games' work remains highly collectable, particularly as most undistributed posters and originals were pulped by government in 1946.
He also redesigned the Cona Coffee Machine, which is still in production today.