I presume if he's not referring to it, he's not talking about it. From a zetetic point of view.
In the first example Rowbotham correctly states that the ball will follow the ship when thrown into the air. It's obvious that he knows of relative motion.
In the later examples Rowbotham states that if your throw the ball into the air while the surface moves rapidly away the ball will be left behind. It is clear that in these later examples Rowbotham is speaking of acceleration.
No Tom, it isn't clear that Rowbotham is referring to acceleration. Rowbotham clearly states that the horizontal motion of the ball is expended at the apex of its trajectory along with its vertical motion.
Besides, a rapidly moving surface is not necessarily the same as an accelerating surface. I guess that we'll have to chalk this up as another example of Rowbotham's poor documentation skills.
Since the word "acceleration" may not have been available to the reader, or available in common usage, Rowbotham must use these examples to convey the concept.
I'm sure that the concept of acceleration, if not the word, would have been well enough known and understood by educated people of the time.