There are tons of posts online from people who were there. It's kind of amazing--I've never seen this much first-hand info on a case before. Basically, here's what they said, from memory.
Couple on the cruise for their honeymoon. They were drinking a ton, and were partying and noisy the whole trip. He made friends with a group of about 5 younger guys (16 or 18 - 20, maybe), and was hanging around them a lot and buying them drinks. She was flirting with other guys.
Night of the disappearance: They were in the disco, him with his guys, her with another group of guys. He called her over and bitched at her for not hanging with him. She kicked him in the balls. He and his friends left. She left later, so drunk she was bouncing off the walls of the hallway. Some say she left with an employee of the casino.
Around 3AM, the guy in the room next to them heard male voices cheering--like a drinking game. Then he heard male voices arguing on the balcony. Then someone saying, OK, goodnight, goodnight, like they were ushering people out. Then voices out in the hallway. Then someone moving furniture in the room next door--really banging it around. Then on the balcony, a big crash--he thought they might have thrown the sofa out.
A woman and her daughter (?) in another cabin heard things too. The next morning, they went on their balcony, and saw the huge bloodstain on the awning over the lifeboats, which was about 4' from their balcony.
One of the stewards (?) went into the couple's room to clean it, and saw a lot of blood. The ship started paging the couple, again and again, and neither answered.
According to one story, the wife said she woke up, saw her husband gone, and went to the gym. Another story says she was "hiding" in the spa when they found her. Others say she was passed out in the solarium, which was by the gym. Someone posted that she asked him directions to the solarium.
About the 5 (or so) guys. They were from Brooklyn. I think they were also Russian, and were there with a larger family group. Some of them were pulled off the ship later for raping another 18-year-old passenger. Supposedly there was a video. But a friend of theirs said online that the video actually exonerated them (it was consensual), and the girl wasn't the one who reported it. They were let go. But supposedly two other women passengers came forward afterwards and said the same thing happened to them.
There was a rumor that they honeymooning guy had been bragging about having $50,000 in the safe in his room.
My theory is that one of the Russian guys, or someone connected to them, tried to rob the groom, and tore his stateroom apart looking for the money. The bride, meanwhile, went "home" with someone else that night.