No, the goal is rarely to kill a monster. The shadowdark (and OSR in general) intention is that the monsters are a danger/challenge to your mission which is not to kill monsters in most cases, but get treasure or reach a quest goal. Killing monster gives you 0 XP, so "kill the monsters" is not the default goal of a dungeon. If you try to kill all the monsters you are certainly reducing the survival chance of your character to a minimum. Avoiding combat should be the key goal for most players, thats why it sound absurd to me if you compare Shadowdark to a video game hack n slash like Diablo.
That is the point, players are supposed to not just run in the room and fight the monsters, because the dungeons don't give any advantages to them. They are supposed to use actual problem solving skills to create an advantage situations for themselves. Or to reach their goal without killing the monsters.
I think the problem that both of you are having that you expect a modern D&D adventure design where the adventure spells it explicitly out if there are other solutions than combat. But the OSR approach is more like: Here is a situation, deal with it, the possible solutions are not spelled out and are just implied. The DM is supposed to be open to improvise to react to the players plans and ideas to overcome a room/challenge etc.