Two things struck me watching this cinematic masterpiece.
First, I was elated to see character actor supreme (439 credits!) James Hong as Miyashima, the Exorcist. And my first thought on his performance was "Oh, he's channeling David Lo Pan from 'Big Trouble in Little China'". But, much to my surprise, I look up the production date of this movie and it's 1984 meaning it was made two years before "Big Trouble". So I guess from now on, when I watch that movie, I'll have to think "Oh, he's channeling the exorcist from 'Ninja III'".
However, I think the most exciting thing to me in this movie was the appearance of the arcade game "Bouncer". For those who aren't 80s arcade nerds, "Bouncer" is pretty famous as a lost arcade game. It was developed by a small company, Entertainment Sciences, and it was quite advanced for the time--"high" resolution graphics, novel gameplay, new technology, see some gameplay here--and tested out in California. You play a bouncer at a bar tossing drunks, flashers, and other bad guys out of the bar. It was on display at a video game convention in New Orleans in 1983 and its appearance in "Ninja III" is probably product placement. But in the end, the high cost of the game and legal disputes between the developer and the company contracted to build it led eventually to all the known parts, boards, etc. being destroyed. It is thought that three working versions might have survived (one of which is the cabinet in "Ninja III") but only rumors of those machines exist (i.e., "a friend of a friend knows someone with one").
For more info on "Bouncer", there is a website dedicated to it (with a long story about one man trying to find one) as well as a Youtube video about it, including a compilation of all the "Ninja III" appearances of the cabinet: