That is odd - for some reason, that property quotes rates in USD. I spent a week in Moscow years ago and paid for a much cheaper hotel room using dollars, but I would think that Marriott in 2006 in Russia would be using rubles.

If they quote you in USD and allow you to book your reservation that way, then they should charge you in USD. Or, like most international hotels I've stayed in, they should quote you and bill you in local currency.

100% in agreement with you: you and Marriott already agreed on a price point and a currency. That's what you should be billed.