These mini-games appear in multiple places within Observer, with 10 of them in all. When you see a terminal, scan through the programs to see if the game is downloaded onto it. Then just play it and complete it. Each new terminal will have a new level of Spiders.
You can find them by just going through each mission, but here's the full list in case you missed one:
Game 1: Room 017
Game 2: Room 017 (same terminal)
Game 3: Janitor's Office
Game 4: Room 205
Game 5: Room 114
Game 6: Room 302
Game 7: Room 104
Game 8: Tattoo Parlour
Game 9: Room 021
Game 10:
Here's a youtube video, all credit goes to the owner:
Be aware that going too far into the main storyline will cut off your ability to return to these terminals, so be thorough as you explore. The final Spiders game is just before the cut-off point. So double back as soon as you grab it if you're still missing levels.