As you noticed there are no place IDs in address components array. You cannot get this information executing only place details request. Developers have already created a feature request in Google issue tracker:
Add place_id in each address_components
You can star it to add your vote. In the meantime the workaround to get place IDs for country and locality consists in executing a reverse geocoding requests for coordinates of the original place ID with result type locality and country.
For example, I have a place ID ChIJEygrJmSYpBIRUXOjvF0QSLw
. The details request for this place
https://maps.googleapis.com/maps/api/place/details/json?placeid=ChIJEygrJmSYpBIRUXOjvF0QSLw&key=MY_API_KEY
gives coordinates 41.3886875,2.130554
. Now I can execute additional reverse geocoding request to get place IDs of locality and country:
https://maps.googleapis.com/maps/api/geocode/json?latlng=41.3886875%2C2.130554&result_type=country%7Clocality&key=MY_API_KEY
The last one gives me
- place ID ChIJ5TCOcRaYpBIRCmZHTz37sEQ (Barcelona)
- place ID ChIJi7xhMnjjQgwR7KNoB5Qs7KY (Spain)
I hope this helps!