Ok pal no I haven't flown a p51, just a piper warrior II. I don't think using all the controls would detract from the game, but I don't think it would hurt it either. In 2008 I hadn't realized how a p51 stacked up against other planes and yes I wrote that thinking things in here were wrong. I was still pretty new to this game. Your quoting skills are noteworthy. To you this is a sim and that's ok man. Yes playing on a computer is a game no matter what, we do agree there. That makes my point though that playing a game does not make you a fighter pilot nor does playing this game. Those guys train for months on stuff and use REAL simulators that move. Navigation, avionics, and so forth. I would say the p51 game in that link would be a sim because of the amount of detail to each system. That is a horrible gunsight in the one picture as well though.
If you guys want to get wrapped up in semantics about what's a sim and what's a game that's fine but the answer is really simple, it's both.
A simulator is intended to reproduce certain aspects of flight. But all simulators have limitations and none of them actually reproduce the total flight experience as much as they represent portions of it to some degree. Some simulators are simple PC based affairs designed just to teach fundamentals (pull the stick back, the earth gets small; push the stick forward, the earth gets big). Some even represent specific airplanes, cockpits and controls like MS Flight Sim but even when talking about the "real" multi-million-dollar simulators with motion bases and full cockpits they still don't really reproduce G-force for instance as much as "representing" it. There are many "real" simulators that are perfect reproductions of a specific airplane's cockpit and performance which are great for instrument and emergency training but are absolutely worthless for ACM. None of the simulators can reproduce the most important aspect of aviation which is you crash, you likely die.
As a basic flight sim to provide an introduction to the principles of flight AH is decent. Someone who "flew" this sim for a few hours would have a basic understanding that would help in actual flight training. Could you spend hours and hours on this sim and then go out and solo a real airplane? Once. On the other hand, it's actually better in some ways than the multi-million dollar simulators (i.e., "real" simulators) for ACM, even the ones intended to teach ACM. That's because you can do things over and over again for hours against other live "pilots." It uses an accurate physics model to reproduce aircraft performance capabilities and it's perfectly acceptable for teaching ACM fundamentals, tactics, principles of energy management and lookout in either a 1 on 1 or multi-bandit environment so yeah, it's a sim.
Is it a game? Sure it is. As Wikipedia defines it: "A game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool." This is basically a perfect definition of AH, structured play that we do for enjoyment with aspects of providing a form of education about WWII air combat. So, the answer is simple, it's both a game and a sim. What's wrong with that?