So what kind of weapons are being fired? Unguided rockets? Torpedoes?

Torpedoes

Yup, those certainly look like the broadside torpedo tube racks used on Japanese surface ships. A few quick Google searches don't find any good images of them, though.

This is the cruiser Kitakami in 1942. A light cruiser fitted out as a torpedo cruiser with 40 long lance torpedo tubes. 20 per side in quad mounts like you see her using here.

As far as I know, she never really got a good chance to use them before being refitted for other purposes (with less tubes).

But if you do naval gaming, and you see a 1942 Kitakami or her sister ship Oi on the table in a game with even semi-reasonable torpedo rules....kill them immediately. Otherwise they will wreck you far more than any battleship can. A battleship will hurt you, but 20 long lance torpedoes will vaporize you. No matter what ship you are using.

World of Warships has Kitakami in it (premium ship). Unfortunately given the way the game works she's currently needing some work to make her more worthwhile to play. I think the next major patch for the closed beta will be giving her smoke like the destroyers in the game, since the ship plays more like a destroyer than the other cruisers in the game.

Her torpedo barrages are brutal, but the chances of being able to pull that off successfully in the game is right now very slim due to easier detectability and lack of concealment that destroyers have in the game. Combined with her having a large critical box, she'll tend to be sunk long before being in a position to strike.