Well, the key does have a transmitter in it to send data, and likely also has a very low power radio receiver, probably kept in sleep mode to reduce current, and this then receives a signal from the car where the power budget is a lot higher so a stronger transmitter than the keyfob, that sends a status byte which probably has a serial number of the pair and a single byte of status and a checksum. 100m is not a problem for a 50mW transmitter, below the legal max for this band of 100mW EIRP, so very easy.
As well the car likely only transmits a few bursts of this data, probably for 5 minutes after you arm or disarm, and the keyfob enables the receiver for a few times after a keypress is sent, so as to get the status, and stores this value, and then when you interrogate it it listens to see if the car is transmitting ( likely will also transmit on alarm activation and manual unlock as well as a backup) and then displays the status, otherwise showing out of range.
Anyway, with 2 CR2430 cells that is a lot of power stored, plenty enough to actually have the fob provide a 50mW transmit power to get the 100m range, though I think that range is only achieved under ideal conditions with a clear line of sight.