I'm not sure exactly what he means or if his being a rich oligarch translates to him understanding what he's talking about.
I think it's quite hard to run out of money entirely. Countries print it, if only for the exchange of goods internally. Many of the people in that country will have no alternative but to use it. But then there will also be dark money markets around the edges using more valuable currencies.
The Russians will still have goods people want (caviar, vodka, grain, oil, weapons) so it will probably be able to sell those to countries that won't be told they can't (eg China, India) in order to buy some of what they need.
But since other countries won't want roubles, Russia will find importing stuff expensive.
I doubt it will actually run out of money, though. With luck, it will struggle and Russians will turn against the war.