The Soviet Union collapsed because the Party lost control of the country and the tensions and outright conflicts that previously prevented any challenge to its power tore up the country. It was conflicts between the nationalities, competition between bureaucrats of different levels over resources, the young Komsomol chiefs against the old gerontocrats, Moscow against the Russian regions, the Soviet Army against the KGB, the religious against the state atheism, innumerable other conflicts, with probably the ethnic/national conflicts having the most intensity. The USSR found out it couldn't control its own population and that is why it retreated from Eastern European countries as well.
The party lost control because of glasnost and perestroika which unleashed all the contradictions and conflict at once, which further caused chaos. It is no accident that the Communist party got itself banned in both Russia and Ukraine. In comparison China didn't try glasnost and did incremental and initially isolated economic reforms, with agriculture still being restricted to family farms to this day.
The USA didn't win the Cold War or cause the USSRs collapse, most of the time the policy was containment or even reapproachment, not rollback.