I grew up on that kind of art… for me it’s just what classic (YMMV on that label) boardgames look like. But there are good and bad versions of it. New Hansa Teutonica is pretty good:
The details are clear, the background is a background and doesn’t blend with the game icons. The style is consistent. The font readable. The colors are clear enough and don’t “pop” too much.
I do like beautiful games, especially beautiful covers. But again what I think is pretty doesn’t necessarily convince the next person. I think quality of art and materials enhances a game for me and makes it more fun. If a game is really great, the art obviously doesn’t matter. But thematic art makes the game come together as a whole more easily. It supports the game while bad art detracts from it.
Art is incredibly subjective but as @VictorViper stated above there are some things about composition and colors that just draw the eye. Many of us can tell these things without explicit training. I think games are not just art though, there is a lot of graphic design here and good iconography is just as important as a pretty cover–even more so. The best game artists make both and are able to blend them into a consistent looking whole.
There is a reason Lacerda games by EGG are so expensive. On Mars has to be one of the best games I have from a art/design perspective (also the game itself is a piece of art–meshing together so many different systems and still achieving a consistent whole that can be played). I cannot think of another atm that is quite so consistent throughout the game.
We can tell when something is cheap because we know the recycled clip-arts and we see the repeated patterns and the bad blending of assets.
