The Genesee & Wyoming Railroad itself is no longer a railroad but a "non-operating subsidiary" of Genesee & Wyoming Incorporated.
The GNWR was merged into the Rochester & Southern Railroad in 2003. The RSR is a class III railroad.
I cannot seem to find an "official" list of Class II railroads (on the STB or FRA websites; it is the STB that actually determines it) but according to Wikipedia it appears that the Buffalo & Pittsburgh would be the only Genesee & Wyoming Incorporated subsidiary that would meet the criteria. All others would be Class III.