Check out the photo below (click on the image for a larger view).
I analyzed the block frame by frame of the slow-motion video. The red diamonds show the path of the ball during the block. The ball starts on the lower right side of the red trail and traverses the red trail until the image you see. One can really see the ball coming in, and then getting rejected!
I estimate that James took off from the court at about 9 mph (14.5 km/hr or 4 m/s) and reached the top of his leap in around 0.4 s. The main part of the block too place in roughly 0.1 s, during which James needed an average force of nearly 14 pounds (62 N) to reject the ball. Instantaneous forces were larger, but 14 pounds is roughly the average force James used to send Splitter's dunk attempt back.
Put simply, LeBron James had to leap to a height that put his hand above the rim, and at 0.4 s to get there, his timing had to be perfect. Once there, James had to push laterally with a force comparable to what one has to exert to hold a bowling ball. Not bad!