Just found this, a better description.
[quote]Pu Zhaozhou, vice-president of the Cross-Strait Aviation Transport Exchange Council, exchanged views with Le Daxin, chairman of the Taipei Aviation Transport Commerce Trade Council, on technical and operation issues on the charter flights.
According to the consensus, non-stop flights between mainland's cities of Beijing, Shanghai, Guangzhou and Taiwan's Taipei and Kaohsiung will be in operation from Jan. 29 to Feb. 20 for Taiwanese businessmen work on the mainland and their relatives to go home for the Lunar New Year Holidays that begins on Feb. 9, a traditional festival for family reunion.
Each side will have six airlines to operate 24 non-stop round-trip flights via Hong Kong.
The two sides also reached consensus on issues concerning crew members.
The charter flights are designed to allow Taiwan business people and their relatives to go home by a shorter and more direct air route. Previously, travelers must stop at a third destination, usually Hong Kong and Macao when flying between China's mainland and Taiwan. [/quote]
Note that the “…via Hong Kong…” means that they will fly non-stop but will fly through Hong Kong airspace at some point in their flight. So the words “direct flight” should really be “non-stop.”