General assumptions: This subsection contains descriptions of all main ways of eliminating the King of Chinatown.
The most obvious way to eliminate the King of Chinatown is killing him while he stays in the fenced area. I definitely do not recommend this solution, because even if you use a gun with silencer or garrote, it is almost certain that you'll trigger an alarm and get the attention of all nearby policemen.
Far better idea is to kill the King of Chinatown in the side alley. If you play on Easy or Medium difficulty level, you just have to wait until two guards leave this area. If you play on higher difficulty level, you have to reckon with the fact that one guard permanently stays in the alley. So it would be good to get rid of this person earlier, stunning or killing him and then dropping the body into a container.
After the King of Chinatown stops in the side alley, make sure that he is not watched by anyone and only after that decide, how you want to get rid of him. Depending on your preferences you can use on him a garrote, a gun with silencer or shoot a chain of the platform above his head, leading to "an accident". Know, however, that the latter option will alert all nearby persons.
A few more ways of eliminating the King of Chinatown are associated with the use of explosives. Your target can be primarily killed by shooting one of the flammable tanks placed throughout the square. You can also find on the map a gasoline can, toss it near the fenced area and then detonate it with a shot.
Another possibility is to obtain remote explosives. These are located in a small weapon shed on the balcony near a luxury car belonging to the King of Chinatown. This place is guarded by a policeman (screen above), so you have to either distract him (by throwing a bottle for example) or wait until he starts a phone call. Then you can get him from behind with proper precautions.
After obtaining remote explosives, you can plant them in any location of your choice. The advantage of this method is that you can detonate them from a safe distance, thus reducing the risk of exposing Hitman.
Since we're talking about a side alley with a car of the King of Chinatown, parked there, an interesting option is activating a car alarm. It will force your target to go to this alley. Wait until the King of Chinatown approach the car and then shoot explosive barrels located behind the car.
A risky way of murdering the King of Chinatown is pushing him into a hole, specifically to into the one shown on the above screen (it is located near the booth at the other side of the square). You have to wait until the King of Chinatown approach the hole and push him (Interact key/button). Unfortunately, there is permanently at least one policeman in the area, so you have first to distract him or be aware of fighting him right after the main action.
The last of main ways of neutralizing the King of Chinatown is using a sniper rifle. This is unfortunately quite complicated process, because first you have to get to the apartment belonging to a dealer. A path leading to the proper building is located on the right of the fenced area and it is shown on the above screen. On lower difficulty levels, there is only one policeman stationing there, but on higher difficulty levels you'll encounter there at least three officers.
An access to dealer's apartment can be obtained in several different ways. If there is only one guard to be sneaked by, it is best to sabotage a right fuse box. Otherwise you might get Chicago policeman disguise (e.g. by eliminating a cop in the alley with the car) and then use Instinct to cover your face. You can also wear dealer disguise - a way to obtain it is described in the next subsection, associated with poisoning the King of Chinatown.
Regardless of your actions, after getting to the dealer's apartment, look around in search for Kazo TRG sniper rifle (should lie on the table). Then move to one of shutters (only the left one is open) and wait for the right moment to shoot. Note - using the sniper rifle will alert all nearby enemies, so hide inside the closet as fast as you can. Also keep in mind that reaching the evacuation point may require killing of at least several policemen.