It is a deck-building game, where players play cards to generate cash to buy cards that go into the deck that they are playing out of (which cycles endlessly). There are 6 boring and fundamental cards that are present in every game, and 10 'kingdom' cards which do interesting and clever things. The 10 kingdom cards that are present in any given game are randomly selected from a set of 25 (around 170 in the expansions), without constraint.
The variations are extreme. Some games have fast drawing and high power curves, some are slow slogs. Some games progress linearly, others build slowly and then explode, and some have stair-shaped power curves because there just aren't any cards at certain price-points. Some games have ways of attack other players. Some games have alternate victory conditions. Some games have multiple paths to victory, other are won by fine-grained control over normally-minor details. In short, the variation is immense and novel experiences have continued, even years after I first started playing.
Can we extrapolate from this? I think so. The two conclusions I would draw are: qualitative variation, and combinatorial traits. Differences in game worlds that are the most interesting may not fit into a slider, and binary or enumerated traits should be considered. Also, the interaction between random variables is what allows for a combinatorial explosion of situations. Stemming from that, it must be the case that multiple variables are meaningful.