It would state that the trail is open to mechanized forms of transportation. I am not aware of anywhere you would be allowed to take a game cart but not a bike and vise versa.
The Wilderness Act states nothing about wheels, it states that there is no mechanized form of transportation allowed.
You can ride horses in Wilderness areas because it specifically states no mechanized or motorized forms of travel. Horses are neither of those. You can ride a pedal bike past FS service road gates because they (generally) state no unauthorized motorized access beyond that point.
This is why trying to classify each individual mode of transportation wont work. There are wheels with IC motors, wheels with electric motors, wheels with pedals, wheels that you push, wheels that you pull...the list can go on, then you can take wheels out and add tracks.
You can simplify pretty much everything down to, mechanized vs nonmechanized and motorized vs nonmotorized.