No, you don’t need the Steamworks plugin if you’re not planning to use achievements, player stats, or leaderboards.
That said, I have five puzzle games on Steam, and from my experience, adding those features really helps. A lot of players actively look for achievements and enjoy completing them, and if your game doesn’t have any, some people hesitate to buy it. I’m saying this from personal experience. Also, using Steam Cloud is a big plus. It allows players to sync their progress and access their save data from anywhere, which is something many users really appreciate.
At first, none of my games had the plugin implemented. But after getting a few reviews mentioning those features, I decided to learn how to integrate it, and now all of them use it. I’ve only implemented Steam Cloud in one game so far to test how the plugin behaves, and it seems to be working well … I haven’t received any negative feedback about it.