I suggest several things. I preface my remarks by saying that I'm sure your girlfriend is a fine humanitarian, frend to all creatures great and small, and a paragon of manners and several other innumerable good traits.
Find a store that allows games to be demonstrated or previewed before purchasing. Try to find the rules online before you buy the game even. You will be able to avoid some disasters that way, and some people just learn better when the gameplay is live and right in front of them.
Allow her some uhmm... rather... all input in which game you purchase, and in the fare for the evening. She might not find the game of the night as appealing as you did, but acquieced to it when she saw how happy or excited getting the game seemed to make you. She might be happy to play Monopoly for the 7.586,574.28 th time. because she is comfrotable with it. Why learn this new game to just kill the three hours of ennui when she already knows the way to Park Place?
I wish I could think of a less demeaning way to say stick to games with simpler rules, but simpler rules need less explination, and it seems it is those moments of explination where she tenses up.
I would find her behavior regarding not reading the rules and then becoming upset when she doesn't understand the rules as perplexing and irrational as you seem to do. I, however, am marrried, and through that, I have learned awhile back that you will see things that are a greater volume and a greater degree more perplexing and irrational, which will appear as you go. Prepare yourself for the notion that perhaps games are just not going to work out sans company to maintain the decorum.
And don't be afriad, either of you, to spend time in hobbies that might not include the other person. Heck, it might one day save both of your sanity to have such harbors while you collect your thoughts and recompose yourself.
If the idea was to find a hobby or activity to do together, there are options beyond books, movies, theater, meals, sports, games, and the usual socitial trappings.
Figure out what the real goal of your efforts truly is, and I bet the problem solves itself.