Why is a toroidal inductor being used in the RFID reader described in DIY FSK RFID Reader?
I feel that a toroidal inductor wouldn't be very effective in grasping the changes in electromagnetic field changes.
Yes, Chris Stratton is right. A toroidal inductor keeps flux within the core, reduces the external flux to near zero and have near zero ability to grasp/convert external flux/magnetic field into electrical signal. Apparently, the word 'toroidal' was used in loose sense referring to a circularly shaped coil.
In an real-life commercial product, a 125 kHz coil typically has many turns on a very thin wire on an open-air core (no core).
An example profession factory made a 125 kHz RFID with a GitHub Arduino library and photos of an antenna coil:
Note, for higher frequency RFID, not shown in above examples, coils have fewer turns than for 125 kHz.