First you have prehistory - the stuff made in the 50s and 60s like Strachey's Draughts, Tennis for Two, OXO and Spacewar.
Then you have the stone age - first two console generations from Magnavox Odyssey to Atari 2600 and everything in between.
Then you have the golden age - the arcade stuff and home gaming from the 3rd generation up until 2007 or so.
Now we're living the greed and anti-consumer practices age - I'd place its start at the Oblivion horse armor and it continues till this day. An age defined by stupid day 1 DLC, lootboxes, microtransactions, always-online requirements, games being far from finished at launch and the ever more intrusive DRM.
I'm sure one could go more in-depth and name more eras of gaming or discern between PC, console and mobile but it's late and I'm not prepared to research and write an essay on the topic. Indie games definitely deserve a mention somewhere.