No. Then it is sauerkraut with chili powder on top. But I will admit that saying there is only one kind of kimchi is like saying there is only one kind of car.
source: my homemade kimchi sitting in my fridge right now has napa cabbage, daikon radish, green onion, ginger, garlic, gochugaru, carrot, sweet rice flour, fish sauce, asian pear, and some other stuff I'm forgetting right now.
And if you add a bunch of chili powder, it's kimchi.