The list of arcade games for Adam's "Challenges" commercial includes two games that are improperly named. There are no arcade games from the era called King of Boxing or Ping Pong. They could be King of Boxer (aka Ring King) and Ping Pong King, respectively.
A game called "Moonwalker" is in the list of games that scroll quickly during Adam's commercial for "Challenges." This is most likely "Michael Jackson's Moonwalker" which was released in 1990, just a bit outside of the show's 1980s time frame.
Opening and closing scenes show "Adam" rocking out to True Colors by Cyndi Lauper, wearing a black wig and playing bass. Given Adam F. Goldberg's age and the wig, it's probably more likely he was rocking out to Alanis Morissette or maybe Sheryl Crow.
This show was set in the 1980's. Wigs like the one Adam was wearing in the video have been sold around Halloween since long before the 80's, and Adam was roughly eighteen in 1990. His appearance in the video is consistent with that time period.