TLDR: Super Mario, World of Goo, Angry Birds.
explain the history of video games
Gotta start with Nintendo & NES, don't you? They whipped the industry in some sort of shape after the crash of the early wild west, and set a lot of precedents still in use today—mainly the developer-publisher relationship and protection of IP. What game represents them best from then?
Donkey Kong is from before the crash, so I go with Super Mario which just shades it from The Legend of Zelda.
Next big thing… I suppose the growth of easy distribution and easier dev—via better tools—which led to the professional Indie explosion on PC in the 00s. Ask 100 people if you want 100 different candidates, so I'll avoid the elephant Minecraft and go with one of my personal favs, World of Goo. Its claim to fame is becoming a major success despite being rejected by all publishers the devs approached—you could say it led the 'growing up' of the Indie explosion.
Final major development so far imo is the online/mobile gaming proliferation, mainly on small devices. Designed for distraction as much as any other attribute, very easy to pick up and drop again at a moment's notice. I'm not familiar with this sector, but I feel a key development it brought to gaming is the freemium and other new monetization methods. I suppose Angry Birds was one of the first big leaders in this new direction, and so beats out Candy Crush.