As Athena53 notes, at many departure airports the local duty free staff will deliver your purchases directly to you on the jetbridge as you board the aircraft.

In other cases, you can take the bottle(s) with you from the airport duty free stores (for purchases that you make inside sterile departure holding areas that are beyond immigration checkpoints).

The obvious concern is that they don't want you to take the bottles and walk out of the airport, thereby "importing" the liquor without paying tax/duty. The whole premise of duty free is that you immediately export whatever it is, and do not consume or sell it inside the country.

So, at places like the USA where there is no exit immigration and no sterile departure holding areas, you cannot be in possession of the duty-free items until "there is no turning back," meaning, once you are physically walking onto the aircraft.

At stations like in South America where they have departure immigration controls, once you pass through you MUST continue to your flight, as there is no airport exit back into the country (unless you went back through arrivals/immigration/customs). As such, they might let you take your alcohol purchases from the store in a sealed bag.

In either case, you would be in possession of the alcohol once on board the aircraft.