Where the Alaska class fits in older cruiser categories

What would the Alaska class have been called if it existed during the First World War?

It would still have been treated as a cruiser, probably a heavy or traditional large cruiser, because its armament and missions remained cruiser-like despite its size.

Displacement alone does not determine whether a ship is a battleship or battlecruiser. Alaska's armament would keep it outside the contemporary battle line even though its full-load tonnage exceeded many older battleships. Cruisers often grew large because they needed range, scouting endurance, and the ability to protect trade routes. Role and relative armament are more useful classification tools than size by itself.