Es heißt "gestern Morgen", weil Tageszeiten nach 'heute', 'morgen' und 'gestern' großgeschrieben werden.

Gnaa, Rechtschreibreform...

Hmm. This purports to be a translation of the English
"were you playing...". But that is a progressive tense,
as was the original Japanese. Is there an equivalent form
in German?

Maybe something like "Warst du gestern Morgen beim Tennisspielen?"

German does not have a true progressive Form.

"Warst du gestern Morgen beim Tennisspielen?" is more like it refers to the whole process: going there, changing, playing tennis, changing again, returning home.

"Warst du gestern Morgen am Tennis spielen" might work, but sounds more unnatural to me that the current translation.

I think both sentences (the beim and the am version) sound like a forced translation of the English sentence. Just like Wolf said, there is no progressive form in German.

In German we only have Präsens, Futur (I & II), Perfekt, Präteritum and Plusquamperfekt. (Oh, there also is Futur III, Perfekt II and Plusquamperfekt II, but mostly beyond standard language.) The tenses only say when the action happened and if it was completed.