Well, Alexei's usage is using initials, it's true. And he used a period after each initial because that's proper punctuation after an abbreviation of even a single letter. I wouldn't make too much of the difference between W, X, Y,& Z, and W,X,Y,Z. We say USA, after all, not USofA(well, most of us don't).
In the case of a diary entry, the four letters of his sisters' names serve to name the sisters. The same as the acronym OTMA does for both its writers and readers. So, you're technically right ; it's not the usual acronym. But Alexei's usage serves the exact purpose as the acronym , namely brevity, and except for the periods, is an acronym. But true, it doesn't support Gilliard's contention of OTMA being a well known acronym for the GDs. It does lend credence to the desire to have an acronym for four girls so often together and thought of collectively.