Fischer most certainly went to Iceland with US national security interests as his primary concern (you really should stop Google before making false assertions to a domain expert).

Henry Kissinger, Richard Nixon's National Security Advisor, called Fischer, and, as an introduction, told him: "The worst chess player in the world calling the best player in the world". Kissinger told Fischer that he should go to Iceland and beat the Russians at their own game. "The government of the United States wishes you the best, and so do I".

The chat lasted ten minutes, and converted Fischer into a resolute patriot. He agreed to play "no matter what", and declared that U.S. interests were more important than his own personal interests. "At that point, Bobby saw himself not only as a chess player, but as a Cold War warrior defending his country," Frank Brady said in the book Endgame.

I already drew your attention to the fact our dual-pronged Cold War strategy of military containment and constructive cultural engagement (helped by Fischer's Chess Diplomacy and the 3 team sports you didn't mention--hockey/ping-pong/cricket) ultimately led to Putin making Russia great again. So Bobby did more than "exactly jack shit to curtail the rise of Marxism" you just didn't understand the modern history of the Cold War well enough to appreciate it. For example, Varna, Bulgaria (where Bobby played a Chess Olympiad) is now free from Marxism. You act like we lost the Cold War; perhaps you were born after it was all over and missed the fall of the Berlin Wall on CNN?

The Cold War was about preventing global thermonuclear annihilation. Your tiresome virtue signals about gays and rooftops is trivial celebrity gossip compared to the actual parameters of realpolitik. Do you want US troops in Tehran making the streets safe for gays to march with 9-year-old drag queen known as Queen Lactatia? Because that's what Team Soros (Pinko Democrats+Tranzi Neocons+anti-West jihadis) want too. Maybe we should let Iranians decide what is or is not their legitimate government, and abandon the hubris of pretending Muh Preferred Ideological Legitimacy is conferred/removed by holding intramural competitions for otherwise boring and unremarkable chess nerds?