I was originally thinking along the lines of using a Steam Auth plugin to tie a users discourse account to their steam account, so you can then gain access to their steam reviews. Unfortunately, by the looks of it, reviews are not something that are available through the Steam API, so that was a bit of a dead end!
Scraping individual user review pages and looking for the boundless appid code could be a way to go, with a manual submission by the user of their steam id/username to get this style link (http://steamcommunity.com/id/stretchious/recommended/324510/). You'd then need a way to process those submissions automatically. I think this would be a lot of hassle to setup to be honest.
Alternative would be to look at modifying something like the "Discourse Solved (Accepted answer plugin)" so that multiple individual posts can be clicked, but only by members of a specific rank. That way, players can submit their review to a thread and a Leader / Admin can then mark it as "Has left Steam review", and they then get their shiny new badge.