Korea. Vietnam. Proxy wars in Afghanistan and Nicaragua. The list goes on.
The war against the Union of Soviet Socialist Republics ended when we forced them to spend so much money on armaments that their economy finally collapsed.
The only "idea" factor that created victory, is that a market economy is much more productive than a command economy. They could not keep up.
The war against radical Islam will be won when we collapse the economies of Saudi and the rest to the point where they can no longer fund actions against us
These were all proxy wars, all despots using communism as a tool to further their intentions.
Islam is a faith, unless you win the ideological battle, the war will never end.