I'm pretty sure the ILS 22R at JFK is still offset. That is, it doesn't actually line up with the runway, and it can *not* be used for a CATIII Autoland. When you look up available approach plates for Kennedy, you'll noticed that 22L has two entries, one for CATI/LOC and one for CATII/CATIII. 22R just has
the one approach. The reasoning behind this is that the equipment is actually located next to, not in line with, the runway due to a wildlife refuge nearby. When landing in low visibility on 22R, the procedure is to follow the localizer and glideslope until the runway is in sight, and then land manually (you'll notice that the ILS minimums are higher for 22R, as well).
22R is primarily for departures, most aircraft land on 22L when JFK is landing in that configuration, and sometimes smaller jets or overflow can use 22R if there is a lull in departing traffic.
As for your parking issue, try using GSX (ctrl+F12) to pick a parking spot, it will tell if you a stand or gate you want is too small for your aircraft. The one in your screenshot is of Delta's commuter portion of their terminal, and normally parks CRJs, ERJs and the like.
Edit: Looking at your screenshot, PMDG's 777 even has the line drawn correctly. You can see that it it not parallel with the indicated runway, but actually draws a slight diagonal across it to the invisible initial fix for the missed approach. When you do an ILS for 22L you'll see that the course is also 225, not 222.