The Malay mancatcher is a trap set by Rainsford that injures Zaroff. Throughout the story, Rainsford is forced to use his experiences and various skills as an experienced hunter to avoid being killed by Zaroff.
The design of this particular trap is that the intended target, Zaroff, will trip the trigger and "the large dead tree, delicately adjusted to rest on the cut living one" will come crashing down and crush Zaroff. Unfortunately, the trap does not work to the extent that Rainsford desires. It only wounds Zaroff on the shoulder.
The Malay man catcher is a trap that is activated by someone activating a trigger. The trap is a dead tree that has been cut and is balanced just right onto a tree that is still alive. When the trigger is activated the person who does so is going to be hit by the tree.