Let's leave aside the carrier under construction for the moment and focus on the container ship and the large tanks starboard of the carrier. The large tanks can be for an tanker or LNG carrier, but they can also be the fuel tanks for an LNG powered container ship. This means that unlike other container ships, an LNG powered container ship is built like a tanker with a series of tanks in the hull, separated with a double hull for safety measures. Given the ships are likely for Europe to Asia sea traffic, which for their size means they are not going through the Suez Canal but goes down the Atlantic to Cape Hope in South Africa, then into and across the Indian Ocean, they would have to carry enough LNG.
A single one of these ships can replace a few smaller container ships that burn dirtier fuel. The move towards bigger ships is reduce the number of ships in the ocean and thus lower the carbon footprint while sheer economies of scale reduce the freight costs.
While gas turbines and electric motor propulsion is an option, the ones that were built used a humongous Otto cycle engine, as in piston engine.