I think you need to modify your expectations a bit.
You think a "visit" is one thing. They think a "visit" is "get together and play video games" it is what it is. If you keep on expecting a "visit" that is more like what you would expect in your family, you will continue to be disappointed and frustrated. If you just accept that the plan is to play Rock Band at least you might not be as annoyed.
This is their method of spending time together. Some do it at events, some do it over sports, some do it over drinks, some do it over food, some do it just them and nothing else. None of those are wrong, and there is no "right" way to do it. You can certainly not go, but to them saying "I don't want to go to just sit around playing video games, i want to actually visit with you all and see you" will likely be to them the same as "I don't want to go to just sit around eating dinner, i want to actually visit with you all and see you" to many others. I think most people are ok with eating/drinking with socializing, for them videos games are their food/drinks.
I personally hate Thanksgiving dinner. The only things i will eat are the Turkey, which i really think only belongs in a sandwich with cheese - straight turkey holds absolutly know appeal to me, and the mashed potatoes, which usually are only edible and not good, as i prefer mine far less mashed then most people do for Thanksgiving. I don't eat any of the other so called "fixings" or desserts. I honestly think a gas station sandwich is more appetizing than turkey dinner. But I accept that for many people, that is what you do on Thanksgiving. I am not going to refuse to go because I don't like the food. That would be silly, I just eat before hand and tend to grab fast food on the way home. I don't see refusing to go because you don't like the games any more justified. That is their tradition, saying you don't like their tradition and means of spending time together is a very thin line from saying you don't like them and you don't want to spend time with them.
I think the idea of bringing a book down is a good one. You could also look for other video games that are more interesting to you. I think that would be a better compromise than a board game.
Depending on the game, you could also look up any Easter eggs/achievements/fan invented challenges/etc. and possibly be the guide master. It might be more fun for you to read things they can do and help them unlock things.