Who says there's no immobilizer in key start car bhai? It does not matter whether its a Push Start or Key Start, most modern JDMs have Immobilizer in it. This can be simply checked by removing battery from the Key and then try to start the car. It won't if it has Immobilizer. Plus there's usually a "Security" indicator somewhere on the dashboard of cars with Immobilizers.
Check this, although this is for Toyota Yaris, so may not hold true for JDMs or other markets.
Another example of the Transponder in Ignition Key system:
