Additionally, I have run a search for the file that is supposedly missing, and it is there, in c:\Program Files (x86)\Addon Manager\Simobjects\Legacy\FSDT_SODE_Jetway_LSGG.
Of course it is, that's what I was trying to say since the start. The problem, I repeat, doesn't have anything to do with GSX or Geneva, or missing files. As I've said, it must be related to a problem with your FSX.CFG file.
You posted the FSX-SE.CFG, which assumes you have FSX and FSX:SE installed in "side-by-side" mode. Assuming this is the case, the file looks file so, the simulator should be able to find the objects. And, in fact, the simulator DOES find the object, because you said yourself the jetway is there, just rotated 90 degrees.
This because it's SODE that cannot find the object, so it cannot animated it properly. But if you see the jetway, it means both GSX ( that has created the jetway ) and the sim, are configured correctly, just SODE cannot find the jetway for some reason.
I suggest posting this on SODE forum.
Please note, it works just fine here, but I only have FSX:SE installed, in single mode, not side-by-side with FSX.