This sentence sounds perfectly fine to me. I wouldn't parse this as exactly a past perfect progressive form, though. Rather, I think it's similar to the past perfect form of the verb phrase "to go X-ing," that is "he had already gone jogging." It carries a nuance of going off to some location for the purposes of jogging, not the action of jogging itself, without a continuous (progressive) implication.
If you were actually using it as a past perfect progressive, it would kind of imply that the action of jogging continued up until the time you ate lunch, and possibly beyond it (progressive), although it certainly started before lunch (perfective). If this doesn't make sense, consider the present perfect progressive with a verb that can't use the "go -ing" construction.
He has been eating (and he hasn't stopped).
In fact, in my opinion the best phrase to use here is exactly:
He had already gone jogging.
He had already gone on a jog.
But preferences may vary by person and region.
As a side note, to me the sentence from the grammar book, "he had already jogged," sounds a little strange. Technically, it does convey that the jogging was a completed action before another past event. But it almost sounds as if he had never jogged before, or that the speaker wouldn't have expected him to have jogged before, probably because constructions of this sort are so often used to refer to the entirety of the past.