Were the wartime King George V ships battlecruisers?

Does the battlecruiser argument mean the Second World War King George V class were battlecruisers?

No. They were designed as fast battleships, and greater speed alone does not change that design category.

The wartime King George V class was built as fast battleships. High speed therefore does not by itself make a ship a battlecruiser. Improvements in power generation helped navies develop fast battleships, with reliable ultra-high-pressure boilers given as the American example.