While, I am inclined to say "game-play uber alles", I am more with Smitchell? your game doesn't need to be realistic or beautifully rendered, but it does need a strong, cohesive STYLE, and looks are a part of that, your user interfaces with the appearance before they ever get to the puzzles.
But style applies to more than just looks.
gameplay style (difficulty, "genre", mechanics, perma-death)
visual style (8-bit, photo realism, cel-shaded etc.)
audio style (bit-crush, orchestral, ambient)
narrative style (text boxes, NPC's, omniscient narration, cutscenes)
It's not one or the other...all these (and more that I probably don't even know myself yet) are necessary, you just need to balance them for the games you want to make to control the experience. It's like a 4-way yin-yang...like a gameplay orgy 4-some where you determine who's on top. lulz.