Incorporated in Sunnyvale on July 20, 1972 (a month after Atari) For-Play Manufacturers Corporation was founded by Henry Leyser, along with Mickey Greenman and Bill Lewis. Leyser was born in Berlin in 1922 to a Jewish family. He studied medicine until the Nazis came to power and banned Jews from public school. Leyser then attended the Berlin Hebrew University until April of 1939 when his parents, seeing the handwriting on the wall, fled with Henry to Shanghai, which, along with Spain, was the only location unconditionally open to Jews. On the ship to China , Henry contracted appendicitis and when the family arrived in Shanghai there were few doctors to be found. Tragically, two siblings stayed behind in Germany and never made it out alive. A brother was caught at the French border and killed and a sister died in Auschwitz. In Shanghai, the Leysers lived in a refugee camp and Henry got work as a deejay. After Pearl Harbor, however, he lost his job when the Japanese Occupation forces forced Jews into a disease-ridden area of the city that became known as the Shanghai Ghetto. With no job and little money, the Leyser's nearly starved but they somehow managed to survive. After the war, they moved to San Francisco where Henry briefly worked as a shoe salesman before getting into the coin-op biz via a job selling shuffle alleys for Mills Sales. He then began operating his own route with pinball games, shuffle alleys, and jukeboxes. After acquiring a few more routes, he renamed his company A.C.A. Sales and Service in 1952. Three years later he merged with a company called BBC. Leyser became famous for his elaborate MOA exhibits. Salesmen would wear costumes with a different theme every day and Leyser would hire the tallest models he could find to pass out literature. In 1965, Leyser negotiated a deal with German jukebox maker NSM to begin selling their machines in the U.S. Jukebox sales were strong at first but by the early 1970s, the market had softened considerably and Leyser was looking for a new line of business. He saw it in the fledgling video game industry. Together with Mickey Greenman (an A.C.A. sales executive and 18-year veteran of United Press International) and Bill Lewis, he formed For-Play Manufacturing. For-Play didn't last much longer after Star Trek. In 1973 they produced a pair of Pong clones - Rally (March) and Sport Center (unveiled at the MOA). They also made non-video arcade pieces like Bio Computer and a dice-themed rifle/wall game called Las Vegas Gallery. By the end of 1973 they had apparently disappeared.
Here's a photo of For-Play's booth at the 1973 MOA show:
 The entire story is unconfirmed. It also appears that the folks at Paramount had failed to secure copyrights to Star Trek themselves and probably had no legal way to prevent people from using the name.
Below are some more photos from the 1973 MOA show. This was the first show to really feature video games. Nutting was at the 1971 show and Atari was at the 1972 show (I don't know if For-Play was there or not) but that was about it, AFAIK.
The 1973 show had several manufacturers. Sadly, I didn't find a picture of the Atari booth.
I have to apologize for the lousy quality of the photos. I got them while perusing back issues of Cash Box at a library. All I had with me was my iPhone and the issues were bound, so I coudn't get any really good pictures.