A large part of the appeal of the original game that was released back in 1994 was that there was no story. Therefore, the player made their own stories up, due to the fact that they personalized and internalized their soldiers' battlefield experiences so much. It was kind of a side effect of being able to name your own soldiers, as well as permadeath.
In this game, there is a little bit of story to set up a framework, but nothing as expansive or intrusive like Xenosaga or Metal Gear. If your wife likes watching video games that are essentially huge as cutscenes all the time, then this probably won't do it for her.
If she's the kind of person who has a good imagination, or likes giving you advice on what to do in a game, then this might be a good game to play together. Give the soldiers names of your friends or people you both know. Even of people you don't like very much. As you play, make up stories and crack jokes about your soldiers as if they were your actual real life associates.
One of my favorite pre-release dev stories was about how the lead producer was play testing the game one day, and all of a sudden he screamed out, "oh my god my mom died", and everyone in the office came over to offer their condolences. They didn't realize that he only just named on of his soldiers after his mom. lmao.
When you're making tactical decisions, ask her for her input, if she likes that sorta thing. Work on your tandem cuddling/controller holding positions. The great thing about turn based games is that you can discuss your next move with everyone in the room. And then blame each other the next turn when everything goes horribly wrong
If it gets boring then go execute Plan B and go have sex instead.