How come mathematicians published in Annals of Eugenics?
Eugenics and agriculture were two areas of application that motivated much of early 20th century statistics. The paper was a continuation of research on the use of Latin squares in experimental design for those areas. It says so explicitly on the second page:
It was, however, only about [1925] that the importance of combinatorial problems, for the proper designing of biological experiments, began to be understood, mainly through the work of Prof. R. A. Fisher and his associates.
At the time, Fisher was head of the Department of Eugenics at University College London.
One should note that in the pre-WWII period eugenics was not the dirty word that it became later. Actually it was a popular notion across the world, including in countries like the United States. The division of humanity into races and the idea that humanity could (and should) be improved by selective breeding was mainstream. Statistics was one of the enabling scientific disciplines and few mathematicians/statisticians of the time would have had moral qualms about publishing in the Annals of Eugenics.
The zbMATH journal profile https://zbmath.org/serials/?q=se%3A00009697 has 137 reviews for documents from this journal indexed in old Jahrbuch and Zentralblatt issues, of overall 49 mathematicians. Apart from Fisher's own contributions, Bose's paper on block designs Bose, R. C., On the construction of balanced incomplete block designs, Ann. Eugenics 9, 353-399 (1939). ZBL0023.00102. mentioned in the question might have been the most influential (at least, it is the one most frequently cited in subsequent reviews).