Takahama was not obligated to seize the cake. She could simply have stood at the doorway and warned Chiaki that if the cake left the room then it would be seized. (At that point, perhaps Chiaki would have tried to smuggle it out, but plausibly someone in the home economics group or even Takahama herself could have suggested bringing the boy to the cake rather than the cake to the boy.)
Takahama stole the cake from her rival. What she did was low.