The movie doesn't have to explicitly be about dragons, but dragons need to be featured as more than just a passing comment or minor cameo or scene.
I love the Eborsisk in Willow. It's a very unique two-headed fire breathing dragon that is somehow both incredibly ugly and very cute, and Willow is one of my favorite films.
Rathalos from Monster Hunter and King Ghidorah from Godzilla are also very cool dragons.
I haven't seen that anime, I definitely should check it out. I was into DOTA briefly when it first came out and kinda dropped out when it became hyper competitive and toxic.
Dragonheart. I said elsewhere that I love that one, but am not quite so enthusiastic for any of the sequels. They just didn't do the original justice.