It should be obvious that as designers, when we design efficiency games we are really designing the inefficiency that the players must grapple with. (Likewise, we don't design balance so much as imbalance.) Broadly speaking, we are always designing inefficiency into games, because games are made up of goals and obstacles, and the obstacles always introduce an element of inefficiency. That inefficiency is what makes a game interesting. However, there are more ways in which designing inefficiency can be a positive thing.
The hobby has a large amount of "efficiency games" where the main focus of play is finding the most efficient (or really, the least inefficient) route to the endgame. But I am struck by how few truly inefficient games are in the hobby—games where the main focus is on the least efficient route. For example, if you play Telestrations as efficiently as possible, the game will fall flat. The disconnect in communication is the fun part of the game. I've not played a published version, but when I play the best players come up with concepts for a starting sentence that cannot be easily conveyed and is inherently silly. This ensures that communication will break down across the game, resulting in very funny reveals.
Clearly, party games have an advantage when it comes to introducing inefficient play, because players take those games less seriously. However, I believe that we could develop other genres of board games to capture different aspects of inefficiency. In video games, we see lots of inefficient play: side quests, achievements, extraneous areas of the map, multiple dialogue choices. Players who "100%" a game are not playing with efficiency in mind. Another type of inefficiency in video games is walking simulators. In these games the goal is not to finish but to experience the environment. And let us not discount the sandbox titan that is Minecraft, where play can continue for years after reaching the end credits.
I suspect that inefficient play in video games is most prevalent in and developed out of solo play. Solo play across all games tolerates more inefficiency than multiplayer. Solo RPGs have also been able to stretch the bounds of what a game can be through journaling and other media, like sewing and drawing. Sewing a map in the RPG A Mending is about as inefficient as you can get, but that is the main hook of the game.
Where solo sensibilities in video games seems to have leaked into multiplayer games, the reverse seems to be true for board games. Solo board games seem by and large just as focused on efficiency as multiplayer games. This seems to be true because solo board games use the same central mechanics as multiplayer but modified for solo play. I don't think we can take styles of play associated with efficiency and try to encourage inefficient play. I think we need new genres of play.
Where should you start, then, in designing an inefficient game? I would start with choosing where I want the inefficiency to be. Competitive play (even in cooperation against the game AI) is inherently efficient in our current cultural context. So I would put the focus on aesthetic play, social play, or creative play. While I think narrative can be a tool for inefficiency, narrative play by itself in the context of board games won't move players far enough away from an efficiency mindset. The goal of play will need to be very clearly something other than winning, such as in Telestrations, where the goal is the funny reveal.
I don't have more advice about how to design an inefficient game that isn't a party game, because if I knew how to create a new genre of play whole cloth, I would be pitching that to publishers. I would like to see board games break into unexpected territory. Inefficiency seems like one place to start.
ShippBoard Games is a board game design blog that updates most Mondays.