airport is a sub-category of transport. Querying for transport will return airports as well, e.g., http://places.demo.api.here.com/places/v1/discover/explore?at=52.559%2C13.2977&cat=transport&app_id=demo_qCG24t50dHOwrLQ&app_code=NYKC67ShPhQwqaydGIW4yg has an airport as the first result.
You can query for the categories valid at a given point. This will return categories including child-parent relationship. Example: http://places.demo.api.here.com/places/v1/categories/places?app_id=demo_qCG24t50dHOwrLQ&app_code=NYKC67ShPhQwqaydGIW4yg&at=52.521%2C13.3807