The Chinese are better at copying technology than creating it. The Chinese Navy currently has a second hand aircraft carrier that was built by the Soviet Union during the final years in the late 1980s. It is not much of a threat because of its age and limited capabilities.
Aircraft carriers can only launch planes designed for carrier use. The Soviet carriers are short and launch the planes using an angled ski deck. There is no catapult, so planes have to use full thrust and not be fully loaded.
The ships are not intended to have the same role as US carriers to project force around the world. They are primarily defensive, with the ability to launch helicopters with anti submarine weapons, and cruise missiles. Protecting an aircraft carrier far from land requires an armada of support ships, and CAP (combat air patrol) to protect the carrier from enemy aircraft, although with more advanced steerable missiles, CAP and submarines may not be enough to defend a carrier.
So China has launched a clone of the Soviet carrier, although it is far from operational – the NY Times source suggests it is three years away from deployment.