From the little I know about history, it seems like Russia has no problem throwing human lives away for the sake of winning any conflict.

Unfortunately very true. And that has already begun, there are already Russian casualties.

What "game" is lost? Nobody is threatening to invade them. Why don't they create better future for their people the peaceful way - pursue math, education, science, even encourage tourism.

Because that's now how a kleptocracy works. Russia is essentially a failed state, a Mafia group with nuclear arms. They simply don't think in those terms, because in that world the people who are currently in power would have no role to play.