It is not easy to know something about this cinema. It is not listed on Russian Wikipedia side Cinemas in Moscow.
It was right in the building of the Hotel Metropol, a famous hotel in Moscow, built in 1899-1907 in Art Nouveau style.
In 1908, a novelty of the entertainment industry of that time appeared - the Opera-Kinemo, later named Modern. It was the first two-hall cinema in Moscow, changed its name in Soviet times into Metropol. Now it is closed.
Here you can see some interesting pictures from the cinema.
It is easier to find this postcard then some information about Cinema Metropol on the internet. I bought this postcard on eBay.