If you're looking for a simple and fun card game to play, I highly recommend Go Fish. You can play it with a standard deck of cards and a minimum of 2 players.

The problem with Ninninjer is that it undersells how cool karuta is (that show undersells itself a lot) by not having any of the team play it professionally like Sena does so you don't get to see how you're supposed to play it and the fact that it could've been replaced by pretty much any other game without affecting the plot.

In Kiramager, it was used to subvert the overly specialized stereotype of fast people by showing how Sena's speed is a versatile skill. Again, this is why Towa often struggled in combat, he was too dependent on being fast on his feet that there wasn't anything else he could do.

Even if karuta isn't for you, it's probably the most excited you will ever get about poetry. Only Japan can do something that unthinkable.