@pkquat, there came a point where RealFlight required certain additional helper components from DirectX 9, making that installation step necessary even on computers that already had the core DX9 installation, or indeed DX11 or 12. But two things: 1) I think that requirement came in after G4.5, and 2) RealFlight would display an error message on startup and simply refuse to run if those components were missing. But it's possible way back with G4 the issues manifested a little more subtly. It's been a long time and my memory is getting a little hazy about that.
Best to simply perform the installation. It will do no harm. You don't need to worry about it doing anything weird to later DirectX versions. You can manually trigger the DX9 installation by inserting the highest numbered G4 disk you have (with earlier CD versions, this should be #4), navigating into the "DIRECTX" directory, and running DXSETUP.EXE.
Another possibility that comes to mind is driver issues. Make sure you have the correct, latest driver installed for your graphics adapter.
It's also possible something got corrupted in your RealFlight .ini or with a custom airport. Try going to your <Documents> directory and temporarily renaming the "RealFlight G4" directory. This will reset everything to defaults the next time you try to run. If it ends up helping, then you can get more selective about discarding only specific things if you care, but it would be a good way to quickly narrow things down a bit.
I do not recommend copying a RealFlight installation from one location to another. You should reinstall from disk and perform online updates. (Feel free to copy the OnlineCache dir to the new installation, though, prior to online updates. It might save you a lot of downloading, and this is safe.)
Re: performance at the clubhouse, there are many variables here. 4K is far more demanding than 1080p. I don't know anything about the specs on that PC, or whether it's working correctly. Sometimes TVs have modes that interfere. That's tough to address this far removed.