.......... Once the antenna is near the intended victimís key fob, the key transmits a low-power signal to the antenna, which is then relayed to the antenna near the vehicle. Once that occurs, the thief can unlock the doors and drive away (if the vehicle has push-button start). ..........
Based upon that description, this method will NOT work against older keyless entry systems, including the ones from the 1980s they mentioned.
This method only works with systems that automatically unlock the doors as you approach the vehicle.
Basically they trick the key into thinking it's near the vehicle and steal the time-sensitive code.
If the vehicle doesn't employ that automatic unlock feature, then this will fail. If you're concerned about this, your user manual may contain information about turning this particular feature off. As long as this feature is disabled at the vehicle, rather than just the key, the problem would then be mitigated.
As long as you can capably use simple RFID repeater hardware to extend the range of the key and vehicle, I don't see a really good way to mitigate such an attack. The only resolve without changing to a different system is to develop/use better ways of verifying the authentic device's vicinity.