Maybe try lowering some settings and see if the card game plays out. I got better performance by disabling nvidia's AA altogether. Some card matches were hanging up to 7 seconds, like it was bottle-necking info. The auto-save seems to cause some random freezing too, though it's more of a quick stutter.
Also, IF you have any cards that auto-play at the start of the round i.e. Sceptor of Storms or similar, maybe try removing it from the deck and see if it'll go forward.
Others have stated setting fire to a row and having a trap on the opposite row i.e. fire on ranged, spike trap on melee row, causing some sort of conflict with the game, which I've run into. Disabling my nvidia AA helped a bunch though. At the time, thought it was the fire's burning effect on-screen eating something up at the higher AA.
If it were me, I'd try lowering things and see if it can get past the area. Also, double-check you have a recent gpu driver and are not over taxxed on your RAM or VRAM.