The Empire's regular military forces aren't that much better than their enemies. In the first episode, the Empire was losing ground to Not-France, until Tanya's battalion came in.

The Empire simply has more powerful and more agile aerial mages. They're the Nanohas to the rest of the world's Harry Potters.

Also, as Tanya was pointing out before she was rebuked, the Empire leadership has begun to spread their forces thin, and isn't aware this is about to become a World War. They think this all ends in a month or two, the not-British kept at bay, the not-French beaten into submission, and the not-Scandinavians made into a puppet state for supplies, and not-Russia won't bother them at all.

In reality, all they've really done is invaded not-France, conquered Denmark and invaded not-Oslo, and completely conquered Poland, Austria, and a few Balkan states.