Usually vegan cheese is just some saturated oil with modified starch, food colouring, aroma and a few other ingredients. However Happy Cheeze is one manufacturer that claims to stick to traditional methods. I did not have a chance to actually try their cheese as it rather expensive, but I do wonder: Why aren't more companies doing this? Is it inherently more expensive? Is cows milk in some way special for cheese making such that we can not just ferment something else and get similar results?
The "traditional methods" for coagulating milk are simply not vegan. It's not the fermenting process but curdling, which typically involves the use of rennet, an enzyme extracted from processing the stomachs of rumiant mammals.
Other methods of curdling/coagulation exist, like the ones used in some kosher or halal cheese, which are vegetarian but not vegan.
Calling the Happy Cheeze methods "traditional" is a bit of a long shot and has more to do with how they market their product than actual cheese making traditions.