I'm exploring the word because I'm intrigued by it, not to honour the author of this annoying use of it.
In fact the word comes from Ancient Greek, ἵππος ("horse") + δρόμος ( "street, course"). So no circularity implied from the etymology.
Looking in cnrtl.fr,
https://www.cnrtl.fr/definition/hippodrome , we see that although historically they seem always to have been circular, including in the early modern period, this isn't necessarily so: "Terrain plat aménagé pour le sport hippique". Then again, the Flaubert quote there assumes that one is able to do
un tour of the thing. So not straight.
Inconclusive, though I'd always seen them as circular (or at least in a loop), and I would bet quite a lot that the author chose this word because, for them, it involves something circuitous, perhaps a round of approvals or appraisals. God only knows.