I don’t think combat is a literal puzzle, just that it feels like it has puzzle aspects, such as clever use of ability combos to set up attacks on big groups or chain attacks on a boss.
That comes from dev comments about how players will find enjoyment in things like how to win combat encounters most efficiently and from the video above.
One example given in the video was using Magik to set up a portal aimed at a transformer(?) box that will stun an enemy that hits it. After that, any knockback attack she does will open a portal automatically that the enemy gets knocked into, then discharged from the other. You can also see examples of knocking enemies or environmental objects into enemies.
The other aspect that I think will make the combat feel somewhat like a puzzle is that the heroes will have a great many things they can do, but you will have a limited amount of options available on any given turn based on the cards you draw. So the challenge is in finding the best use for the resources at your disposal.