Well, they seem to be programmed to eat only moving objects. At least part of the object needs to be moving, even if it's only the antennae. I don't know if legs count, necessarily, as our chams won't got for a roach that has fallen and is laying on its back with its legs waving wildly.
It seems the chams are wired to go for reasonably healthy prey.
In general, however, it seems to be movement that gets their attention. They would have no reason to recognize a stone-still cricket because it would not get their attention in the first place.
Just some thoughts.