I think it might for some. Those that had their hearts set on an all of one type team (like a fire theme for example) would probably need to reconsider and choose a team that's more balanced for battling. I doubt Blizzard would make attack types work ONLY against one other type of pet, but I'm going to guess that to be the most effective, you'd want to have a healthy mix and match of spell types just in case you run into an unexpected pet in combat.
I'm curious to find out just how "good" and how "bad" each attack is when against the corresponding type. I mean... a critter attack can't be completely useless against a humanoid pet, or else that would mean boxing us into a very specific style of gameplay. Hmmm... more waiting and wondering for now.