When you view a red shell enabled ad, a script on the page (or perhaps the ad server itself, based on HTTP headers) computes a fingerprint of your browser (IP address, browser version, fonts installed, screen size etc.) and stores (ad_id, fingerprint) in a database somewhere.
When you install and run a red shell enabled game, it computes the fingerprint of your machine and sends (game_id, fingerprint) to the server, which stores this in another table.
By joining these tables on the fingerprint, you can get some info on which ads are correlated with which game purchases.
Apart from this, red shell does NOT modify your browser settings, inject code into all pages you visit, add a browser toolbar, constantly run in the background, MITM your TLS or anything else like that. [EDIT: not trying to defend red shell here, just checking whether I need do a full reinstall of my PC to get rid of this thing]