These all revolve around the titular wooden dummies from Shaolin Wooden Men. In their original appearance, they are 36 mannequins moved from beyhond walls using chains, and they are used in the test of the "Shaolin Wooden Men Alley".
Tobal No. 1
August 02, 1996
Quest Mode in Tobal No. 1 features an enemy called Puppet, who is likely based on the titular dummies from Shaolin Wooden Men, since it looks almost exactly alike. The most notable differences are Puppet's trunk being composite of two pieces instead of a big one, its face sporting a long nose and two green leaves sprouting on its head. Puppet also has no chains, since it can move on its own.
The game also features a stronger variant called White Puppet, that comes in a very light shade of brown.
Puppet returns in Tobal 2, and this time there's a blue transparent, squarer version called Box Man. Like all other enemies in the game, Puppet and Box Man are unlockable as playable fighters.
March 22, 1997
Tekken 3 features a secret character called Mokujin, that is likely based on the titular dummies from Shaolin Wooden Men, since it looks almost exactly alike. The most notable difference is in its head, that features a long nose and two green leaves sprouting on its head. Curiously, these traits were already featured in Puppet from Tobal, possibly meaning that Mokujin was partially inspired by it, even if it seems unlikely.
Its second player outfit is a female version of it, featuring a flower instead of leaves on its head.
Mokujin also appears slightly different in gameplay rather than in CG cutscenes: in gameplay it has no eyes, and only has chains connecting its arms to its forearms, while in its ending cutscene it has round glowing eyes and has a chain connecting its forearm to its trunk, actually resembling the chaing that move the puppets in Shaolin Wooden Men. This design is also used in an official artwork that later served as its character portrait in Tekken Tag Tournament, only this sports little square eyes only carved in its head, once again resembling the facial features of the puppets from the movie.
Mokujin returns as a playable character in every later installment of the Tekken series except Tekken 4, and also makes occasional cameos outside it. A totally metallic variant called Tetsujin was also included in Tekken Tag Tournament.
In Tekken 5 Mokujin was slightly redesigned, this time featuring loose chains attached to its forearms, hips and ankles, possibly making it more similar to the puppets from Shaolin Wooden Men.
Tobal's company Square as well as Tekken's Namco had no right over the puppets from Golden Harvest's movie, in fact they only created original characters slightly inspired on the puppets.
Likely, Namco had no right to use "Puppet" from Tobal, but they only used some of its traits, given that it wasn't a coincidence.