Even in game, a good destroyer can and will make a battleship her bitch in a night battle.
First, in real life, the destroyer will never defeat the battleship - never, even at night. The caliber of ammunition will destroy any destroyer in a matter of seconds. On the main caliber - I'm silent. Secondly, Russian blood flows in their veins - therefore, they always solve all the differences and there can not be serious conflicts between them! Enough to fantasize!
Any post-Fubuki-class destroyer can sink a dreadnought era battleship like Gangut if they can hit with a spread of torpedoes. Just like they sink when hit with a similar spread from a submarine.
Later era battleships it becomes more difficult as the subdivisions and anti-torpedo blusters get better, along with the anti-destroyer weaponry getting better, and by the era of the Fast battleships or Yamato, battleship can absorb several torpedoes without sinking, while also being able to track and sink destroyers much quicker at ranges outside torpedo range (unless it is a Long Lance, but the battleship can still likely hit the destroyer outside of normal torpedo combat ranges, as oppose to the actual maximum range of the Long Lance, since most destroyer commanders didn't launch at those ranges)
But a 1909 designed dreadnought? No. The Gangut-class was very weak against torpedoes and mines until their 1930s to 1940 reconstructions gave them some more bulkheads and anti-torpedo blisters. But when built, she didn't have any anti-torpedo bulkheads. She was designed to fight and defeat the Japanese battleships (pre-dreadnoughts) from 1905, combat shore batteries, and outrun the German battleline for the advantage of position. In the Baltic there were mines, but it was mostly Russians laying them. The torpedo threat was not high at that time.
The main threat by World War II in the Baltic was airplanes, and this class suffered from them.
But in the Pacific, where these ships never went, night battles around islands make for a very dangerous place when it comes to torpedoes. Particularly if they are Japanese torpedoes. And unreconstructed Gangut would probably not be able to survive a single torpedo hit from a Long Lance that Hibiki would normal carry in Japanese service.
