Basic idea is to have the community all play the same game and then talk about it and our experiences.
I feel the games should be either very inexpensive or free. Even a demo or "Prologue" would be an easy way to make it free. In regards to selecting games we could use community engagement and vote in some fashion, or have a pool of games which everybody contributes to and one is selected at random.
This is just a random idea I had but wanted to throw it out there.
There's already a Gameclub on the official Patient Gamers Discord (https://discord.gg/patientgamers). Every month they choose a Long Game and a Short Game to discuss and play together. This month's games are Hotel Dusk and Hitman: Blood Money.
If you're on Backloggd, there's also the unofficial Backloggd Discord Game of the Week, with a greater focus on weird/obscure short games.