While that particular attempt had a purpose (to advertise the Hotel and raise money for a good cause), there's probably a reason it has stood for 60 years, mainly that it would serve no real purpose any more. It was a bold idea, the right guys at the right time in Aviation History. I'm not an aviation history buff so it's not surprising that I've never heard of them or the flight, but I also don't imagine that it's the topic of normal conversation around a keg at your local GA airfield either.
As for going for it in FSX or P3D or X-Plane, it's certainly not impossible, but certifying the flight. . .that might be a different subject altogether. No more than two people (must be the same two people that start the flight) flying constantly for at least 65 straight days, flying a Cessna 172 and using the Duenna to validate the entire flight and show that the aircraft was flown "non-stop". Refueling would have to be done "on-the fly" using a keystroke to invoke the action of topping off the fuel because I believe if you used the drop down menu for Fuel and weight it would show a pause in the Duenna which would invalidate the flight (maybe someone can advise if that's the case or not).
Hmmm, come to think of it, even one refueling might invalidate the flight, regardless of how it was performed. Oh well! Maybe there's a daring duo out there that might take it on, but considering we can't get folks to use the flight server here at SOH for whatever reason. . .finding anyone who has that amount of time to kill might be a stretch. Good Luck!