Not sure how you add your Steam ID on the list, the form only allows for link to it.
The google doc seems a bit messy, might have been easier to keep a google doc spreadsheet?
Tabs would have the different platforms: Origin, Steam, UPlay, Battlenet, Arc, Other Games.
Something like this?
https://docs.google.com/forms/d/e/1FAIpQLSc_vun2HN7_GLj_aCb7-lEvPuoDG9_bceZO7_qqSwWYrRN9lw/viewform
An you can then see the results like this:
https://docs.google.com/spreadsheets/d/1ZJTmqlE24vrmq6_f_DwnFG2MHex05EhOGp-7rvXAv78/pubhtml
Some of the games not on the list: MechWarrior, The Crew, Division, Star Trek Online, World of Warcraft, Heroes of the Storm, Overwatch, EVE, PayDay 2, Marvel Heroes, Grim Dawn, Titan Quest, Battleborn, Dying Light, Smite, DOTA 2, Warframe, GTA 5, Borderlands Pre-Sequel, DAI, How to Survive 2, Zombie Trilogy, World of Warships, Dirty Bomb, Tom Clancy's Rainbow Six Siege, Star Wars Online, Dreadnought etc etc
)
The best an most lazy way would be to just have the 1 Question and let the user input the games they play (Steam Games [FREE TEXT]), otherwise you would have to constantly update the list, this way it is pretty much self sufficient. You can do a cleanse once a year or something, just extract the spreadsheet and use MS Office to clean it up then reupload it. Anyone looking to add ids can just perform a search for the game name and copy past user ids as necessary.