The history of game design isn’t one story. It’s a set of overlapping stories, with each genre having both recognizable eras of its own and links to larger, genre-spanning ones. Often these stories spread across time (thousands of years, in some cases!), across physical distance (Europe has its own video game design tradition, which looks completely different from the USA’s–but is little known here), and across academic fields (can the Metal Gear series be fully understood without taking a biographer’s look at Hideo Kojima?).
While the complexity of design history can be daunting, it hints at the incredible rewards to be found when one plumbs its depths. Every designer stands on the shoulders of giants, and there are so many more giants to stand on than we normally imagine! You can call upon giants in entirely different genres, or even seemingly-unrelated fields! The interconnected history of game design creates many, many vantage points from which one can analyze a problem and seek solutions.
Games influence, and are influenced by, lots of things. Avoid myopia; your understanding of games and genres increases the further you zoom out.