I’ve never played the GW 1936 and 1939 games mentioned by Xlome_00, so I don’t know how they handle the Comintern angle, but in terms of Global 1940 I think that the best option for handling the “Comintern third faction” concept would be as follows (after I’ve covered some necessary background).
As I mentioned previously, the actual course of WWII does indeed support the notion that the three major Allied powers – the US, the UK and the USSR – weren’t a unified block but rather two factions (the Anglo-Americans on one side and the Soviets on the other) who cooperated for reasons of convenience/necessity, but who essentially fought their own respective (and in many ways separate) wars against Germany. The separation wasn’t just in terms of geography (the Anglo-Americans in the west and the Soviets in the east), it also existed in terms of methodology and philosophy. The Anglo-Americans devoted huge resources to naval warfare (since their countries were separated by the Atlantic) and to their strategic bombing offensive against Germany; in both cases, this reflected a “capital-intensive” approach to warfare which emphasized technology and hardware and which was relatively economical in terms of manpower (both in terms of forces deployed and of casualties taken). The Soviets certainly didn’t neglect technology (as evidenced, for example, by the T-34 and the Sturmovik, both of them superb fighting machines produced in vast numbers), but their approach to warfare was basically “labour-intensive”. This approach reflected three things: the primarily land-based nature of the war on the Eastern Front; the Soviet Union’s vast manpower reserves; and the willingness of Stalin and his commanders (including Zhukov, who was brilliant but also quite ruthless) to sustain massive casualties.
Also supporting the “two factions” concept is the fact the the USSR and Japan were at peace for most of WWII, even though the US and the UK and the USSR were all fighting Germany, and the US and the UK were both fighting Japan. This state of affairs led to some odd – but under international law, legitimate – situations such as American B-29 crews being interned by the Soviet Union when they made emergency landings there after bombing Japan. There’s also the fact that the US, the UK and the USSR, even while they were fighting the Axis, were keeping an eye on the eventual post-war world and were trying to “preposition” themselves for this new world order. To give just a few examples: Churchill (among others) wanted the Anglo-Americans to take Berlin out of concerns that the Soviets might end up dominating postwar eastern Europe (which they did); the Russians allegedly alerted Japan about a planned US carrier strike against Formosa because the Russians didn’t want the Americans to win the Pacific War too quickly; and the Americans were determined to occupy Japan before a single Soviet soldier could set foot on Japan’s home islands, in order to put Japan firmly in the orbit of the US after the war. (It should be noted that these “prepositioning for the postwar world while still fighting the Axis” maneuvers between the three great powers were basically the same thing that Mao and Chiang did in China from 1937 to 1945.)
The point of all this is to say that treating the USSR as its own faction in a Global 1940 game is perfectly valid from a historical viewpoint. As far as the “Comintern” angle goes, however, I’ve previously noted that the term refers to a political movement rather than to a country, at least in a WWII context. (The Cold War is another story: the Soviet Union, the other Warsaw Pact nations, Red China, plus North Korea and North Vietnam, add up to a lot of countries, a lot of men and a lot of military hardware.) So in Global 1940, “international Communism” (to use a less problematic term than Comintern) should probably be seen not as a freestanding “player power” (with its own map territory and its own military forces) but rather as a special ability (a bit like a tech build). Moreover, this special ability would be restricted to the Soviet Union, and it would be an ability of a political nature rather than a military nature (like one of G40’s political rules). I’m not sure what its precise nature ought to be, but one idea would be allow the USSR to potentially tip neutral nations into the Soviet camp by encouraging communist agitation within those nations. It should probably work like a tech roll (meaning that the outcome wouldn’t be guaranteed), and it should probably only be allowed once in any given country (because a failed communist uprising would presumably result in a crackdown by the government). The probability-of-success dice tables should vary for different types of countries, with the highest probability of success being for the pro-Allied ones, the lowest for the pro-Axis ones, and intermediate for the strict neutrals. The ability should be restricted to the USSR because in WWII only the USSR was in any kind of position to “export communist revolution” to other countries; this wasn’t the case for Mao, who was arguably trying to import it rather than export it.