Already the 5th book in this Crosstime series! Turtledove has impressive if not prodigious productivity. Commendable how this book continues the trend of describing a timeline quite different from those in the earlier books. Reading across the series, there is an unpredictability in settings that can be an attraction to some readers.
By the way, here there seems to be a slight reference to Turtledove's first big hit, The Guns of the South. The latter was also about alternate universes. In which the logo of Apple Computer was described. Also done in Gladiator. Turtledove probably put the remarks here, simply because a reader could recognise it, without him having to explicitly name the manufacturer. But maybe he's also reaching out to his earliest fans.
Another person who reviewed this book was spot on, hilariously but accurately, in labelling it "mission creep". An interesting development harking back at policy changes in the parent world.
Unfortunately, the narrative, in the combination of both the spoken dialog and the thoughts attributed to various characters, is often weak. There is a structure often present, usually involving a statement immediately followed by a counterpoint or negation of that statement. If you haven't noticed this, try rereading and parsing carefully. Once you see it, then you see it everywhere. Also true of the author's other works, like his 10 or 12 volume Civil War series. But in this book, the repetitive structure seems especially pronounced. As though he is dumbing down the narrative, for a young audience. Or that he is not putting enough effort into writing interesting prose. It can get stale to read, after you notice.
By contrast, look at Rowling's Harry Potter books. Also ostensibly for a similar audience. However the narrative flow is far more varied and interesting to read. You cannot easily deconstruct her works to detect a simple narrative pattern. Also reflected in the marketplace. Her books outsold any in the earlier Crosstime series books, probably by over an order of magnitude.
Granted, the typical reader of Gladiator probably will not consciously notice the repetitive structures. But unconsciously, this may be subsumed and expressed simply that the book is "ok but not great". And ultimately in sales. A pity, because Turtledove's series is a great idea, that deserves stronger expression. We need a successor to Piper's Paratime, and this series is the closest active approximation.