Did the communist government of Russia want to spread its ideas through world revolution?

Yes it did, because according to Karl Marx, the proletariat would be a class of workers with no national affiliation when it rose up against its bourgois oppressors. It was felt that a single communist state could not exist for long in the midst of capitalist nations. For this reason, socialist/communist activity was encouraged by Lenin and Trotsky so that there would eventually be more and more socialist/communist countries.

In order to foment such revolutionary activity in other nations, Lenin created the Communist International. This organization, led from Moscow, funded, organized and coordinated revolutionary activity in other nations.