"Ich war am Spielen" is not really Standard German. It's a West German/Ripuarian dialect form that people from that area sometimes use when conversing in Standard German. But yes, it does communicate the progressive aspect in the same manner that "I was playing" does in English. I agree that "nouning" the verb is an arbitrary distinction.

Even if you want to give this one to German, English also has the prospective aspect, which is missing in German (prospective "I'm going to play tennis", vs. perfective "I will play tennis").