I think the third party software simply pushes the aircraft position/settings data into the sim to essentially override the in sim live calculations. So it replays the flight “as is” ignoring any inputs from the sim completely.
Strange things can happen though. So if you are replaying and in the replay interact with the controls using mouse or mapped buttons, you can definitely confuse things. Also I don’t think everything is recorded in terms of inputs- eg garmin programming. No flight plan is loaded in the FMC.
It of course doesn’t record weather or other planes etc.