So, the article states that Steam release supports cloud saves, which contradicts the game's Store Page (it is not listed as a feature) and Steam Community discussions. So I installed the game on one machine, played it a little bit, then installed it on the other machine, launched it, and saves did not transfer over. In the main menu there is only New Game option available, the Chapters option is grayed out. If cloud saving via Steam is possible, but it requires config editing, this should be pointed out in the article.
Topic on Talk:Wolfenstein: The New Order
Well, SteamDB at least confirms it is using cloud saves (https://steamdb.info/app/201810/ufs/). When I used the game, it clearly stated in Steam it was uploading information to the cloud. Never tested if the saves actually did transfer. Both your machines were online and synchronized the cloud information right?
Yes, both machines were online, and cloud saves work correctly (in the Binding of Isaac: Rebirth at least).
Also, I want to point out that certain games have Steam Cloud pages in SteamDb, but they do not utilize this feature (e.g. Dark Souls III).