This app was mentioned in 5 comments, with an average of 1.00 upvote
I vaguely remember having games on my 1st gen Nook, but I haven't played games on an eink based reader since then. It had a chess game too.
Now that you've got me thinking about it, my Boox Note is able to run this Risk knock-off (link is to free version, but I already own the paid version).
I've got it set to the "Paper" Game board graphics style in Options and have Play icons set to "By player". It's easier to follow if you enable "Fog of war". A2 mode doesn't seem to make much difference. Sound effects help you keep track of what's going on with the other players better.
I would definitely recommend border siege. There's a lite (free) version, or the full version for $1.50. It's got multiplayer, over 50 maps, and the developer is really attentive. I've been playing it for years and I think it's the best Risk app out there, especially for the price.
get them both on google play: Border Siege Lite (free) or Border Siege full version ($1.50)
There's an Android version of Risk that includes Tamriel as a map.
I'm pretty sure the Risk: Global Domination game does not have the local multiplayer you want. It does say it has pass and play, so if you're all together, that would work. The game has IAPs for different maps.
If you don't mind trying a couple out, you could see if Border Siege (used to be called Drisk), Rise Wars or Domination work for you. They all describe having a pass and play / hot seat option, but I didn't see any with local multiplayer. They all have a free version, a couple have a paid version.
Re: introvert. I understand, I'm a big introvert myself. It wasn't something I'd normally do. One of the best things I did was a tour of some Mayan ruins where it was just the tour guide with me and my wife. He did a great job avoiding the big crowds. We had good experiences with third party excursions. Hope you have a great cruise!