I installed the game on my second pc just now; It downloaded the cloud save, then I launched it. At the game menu, it gave me unlock notifications of stuff I had already unlocked on my first pc, but I noticed there was only a few unlocks. Then I tried starting a game and saw that much of what I had already unlocked was still locked on the second pc, example with a locked deck even though the game "knows" I beat the white stake with it.
The collection is also wholly incomplete compared to my first pc (on which, for example, I have discovered all booster packs).
One thing to note is that I did play the demo on this second computer, maybe the game prioritized the demo save's data over the cloud save?