For me, playing video/computer games without sound is kind of like watching a movie without sound. There are some movies that you don't need sound to fully appreciate. Like most silent movies. The same goes for video/computer games. You don't need it for games like Battle Chess, Dominion or Hearthstone.
But to me, playing Heroes of Might & Magic III without sound is like watching The Godfather subtitled without sound. And as mentioned some games have pretty distinct audio cues, which makes them almost unplayable without sound.
All that aside, the guys working with the music and sound effects also worked on the game. But I guess the graphics guys are more important?