I'm not entirely sure what you are referring to. You might be referring to the fact that the author's definition of big-O doesn't say anything about constant factors or asymptotics. This makes the definition incorrect, or at least sloppy. But judging by usage, it seems that he actually knows and is using the standard definition. The error is just in that one sentence, and it doesn't affect the rest of the argument.
You might also be objecting to the fact that he makes a distinction between time and instruction count, and is using big-O notation for both. I don't think there's anything nonstandard about making this distinction when it needs to be made. Take, for example, Karmarkar's algorithm:
