You wouldn’t necessarily choose to say that UX Design and boardgames have much in common. Maybe you might stereotype boardgame players and UX designers in very similar ways… but not much beyond that.
One thing connected these two things is Hick’s Law. As described in this article, Hick’s Law states that the more decisions there are, the longer it will take for someone to make a decision. Now, this may not come across as revolutionary, but consider two things: it was the 1950’s and, even for obvious things, there needs to be evidence for it to be considered scientific.
This relates to UX design because when looking at choices on menus, it is important that someone doesn’t get frustrated; it promotes minimalism in design choices. This relates to boardgames because it is frustrating to make decisions and games that are overly complex are a turn off. Laws of design are almost universal. They affect all types of design – not only one aspect of it. Different types of design may not matter when it comes to this.
It can be argued that making decisions is the point of boardgames and that people turn to them for complex scenarios, but people don’t do the same with menus. However, if something is too complex for the medium its in, the result will be the same: people will not pay attention and the design will be looked at poorly.