So we can help you out from your confusion: Within the post-WW1 super-Dreadnaught era, a battlecruiser refers to a ship with a caliber of at least 13.5-inches without the armor to defend against said gun for the sake of speed. Given that the Alaska was specifically designed with 12-inch guns and to be immune against said 12-inch guns, already it defies what a battlecruiser is. It's not even fast enough to escape a regular battleship, never mind have the armament to do anything against a BB. Heck, RN made it a specific goal for battlecruisers to be at least 5 knots faster than contemporary battleships.
More importantly, the Washington Naval Treaty definitions are not something that are written in stone. They were specifically arms race limiting restrictions, and have nothing to do with actual functions or roles. To refer to them about how to classify ships is not understanding why those classifications were made in the first place.
For more information, you can check this thread or this FTR article. In addition, here are specific post excerpts from the first link:
Although to be completely honest I could have, and should have, gone into far more detail then I did.. I actually cut out a lot of stuff most of which was extra technical. Or operational related.
Also the ship really is a Large Cruiser. It is NOT a Battlecruiser nor is it a Fast Battleship or "Pocket Battleship".
It really is its own class of Cruiser.
Well, chasing something down is a lot of math and its not just flat out speed.
At the cold and hard end of the day, catching the opposing battleship matters very little because Alaska cant take the hits. Sure, it could catch a battleship... eventually...
(Iowa going flatout 30.3 +-0.3 knots @ 196 rpm for 4,710±140 nm Radius (56,500 tons displacement)
(Iowa is actually listed as a 57,100 tons avg displacement if you wanted to get more technical)
(Alaska going flatout 30.5 +-0.5 knots @ 254 rpm for 3,390±150 nm Radius (33,650 tons displacement)
(Alaska is actually listed as a 33,800 tons avg displacement if you wanted to get more technical)
(South Dakota going flatout 27.1 +-0.4 knots @ 181 rpm for 3,900±170 nm Radius (45,800 tons displacement)
Now do you see the problems with chasing down a Battleship? Mind you the data above is from wartime conditions. And we haven't even covered the sea keeping abilities of both ships.
Source: War Service Fuel Consumption of U.S. Naval Surface Vessels. 2ed ed. G.P.O., 1947.
United States Naval Administration in World War II, Bureau of Ordnance, No. 75 Guns and Mounts... in the post war refers to the ships accordingly:
b. History of 12"/50 Three Gun Turret
The design of the 12"/50 three gun turret was undertaken at the instigation of President Roosevelt when he requested the Bureau of Ordnance to investigate the size of gun capable of combating German cruisers of the Deutchland class. The Bureau made a number of preliminary studies of 10-, 11-, and 12-inch, one gun, two gun and three gun turrets before a final decision was reached to develop a new 12" gun. The original design called for four turrets--- two 2-gun and two 3-gun 12"/50 turrets. The design was carried out to the preliminary procurement stage when the decision was reversed. It was decided to put three 3-gun turrets instead of two 3-gun and two 2-gun turrets on ships of this class. The main reason for this change was to have all the turrets alike in order to simplify the manufacture and procurement of associated equipment.
The ALASKA was the first battle cruiser built since the first World War. The main difference between this type of ship and a battleship lay in the thickness of armor. For this reason the battle cruiser was lighter and therefore had greater speed. At the beginning of the program in 1940, plans called for the building of six cruisers of this type, with the USS ALASKA as prototype. The number was later reduced to three. Actually only the ALASKA and GUAM were finished in time to enter active duty with the fleet. The HAWAII was under construction when hostilities ceased but was scheduled to be finished and placed in the inactive fleet.
Although the reality is that the Alaska is a Large Anti-Cruiser capable of out ranging anyother cruiser(gunnery), out roaming (radius of action) and capable of independent operations. Unlike a Battlecruiser which is going to be tied up with larger numbers of other ships. It is the Anti-Cruiser role that people generally tend to forget. Putting the Alaskas up against other Medium to Heavy cruisers would probably work out in Alaskas favor... Against a battleship is just complete suicide with no remotely positive outcome at all.
I hope CCs can educate themselves before making historically inaccurate statements.