A nicht at the end of a clause means the verb in second position is negated. So, in
Eine freie Presse gab es nicht.
the predicate is nicht geben. That's slightly different from
Es gab keine freie Presse.
where eine freie Presse is negated.
In your example, there is little semantic difference. The reason why the first form was used is the special position in front of the clause. It's the topic. The alternative
Keine freie Presse gab es.
which has the negated freie Presse as the topic sounds off. There's even a pun using that for effect:
In a former GDR Kaufhaus:
Haben Sie denn keine Schuhe? — Hier gibt's keine Hosen. Keine Schuhe gibt's dahinten.