Literature on the A300's spoilers is lacking, so is the flight manual's description. But based on publicly available information, there is a very strong candidate for a reason.
The A310's wing is very different from the A300's. Of the relevant differences, the A300's wing is:
- Thinner (you can also visually tell: wing thickness under the deployed spoilers and spoiler thickness)
- Outboard section having double-slotted flaps (not on the later model -600R shown in the question)
Three different A300/A310 flaps, and A300 v A310 wing thickness
Both of which when combined would lead to a spoiler mechanism packaging difficulty, which leads to smaller spoiler actuators. The A300's spoiler with a gap would lessen the low pressure behind the spoiler, making it easier to deploy and hold.
In fact, the inboard spoilers where the wing is thick, the spoilers are normal:
— Lufthansa Airbus A300 Landing Berlin Tegel (YouTube)
Another airliner with such a gap is the Caravelle VI-R. The gap is referred to as a breather slot:
[Spoilers] require holding open as the airflow tends to blow them closed. Some [spoilers] feature breather slots, e.g. the ones of the Airbus A300 and Sud Aviation Caravelle.
1: Airbus FAST magazine #5 (PDF)
2: Aerodynamic Design of Airbus High-lift Wings in a Multidisciplinary Environment (PDF)
3: Alternative Air Brake Concepts for Transport Aircraft Steep Approach (PDF)