Ricks' observation (and I'm going by Sigger and Farley's summary of it instead of going back to The Gamble because I'm lazy) is that General Petraeus doubled his physical training in order to prove to the promotion boards that a braniac could compete in the physical realm with his less academically gifted peers.
I'm not quite certain that's the case.
Every officer evaluation does have a spot for the rated officer's physical fitness...only it simply says "Pass" or "Fail". Passing with a 180 (the minimum passing score) counts just as well as a 300 (the highest possible score) for the purposes of an evaluation. There might be comments in the officer's narrative, but this hardly gets any attention. Only the tiny block for the comments for an officer's senior rater--the one two levels of command higher--carry any weight at the board. This block only allows for two sentences at most--and metrics such as marksmanship scores and physical fitness scores are usually absent.
However, there are a few good observations one can draw from General Petraeus' fitness obsession. I would say the first is that the endless running General Petraeus does might be his "alone time", where he finally gets to think. Despite the fact that long-distance running might not be the best warrior workout (you'll have to go to Crossfit for that), it does allow for uninterrupted alone time, which is why I like it. I would think that someone like General Petraeus would thrive on an hour of quiet contemplation and meditation each day.
Secondly, I've also noticed that the US military's attitude towards fitness differs greatly from that of many other militaries. I've encountered a number of generals who feel obligated to remain in tip-top physical condition, in order to serve as a good example for younger troops. Indeed, in the US military, it's expected that commanders be in better physical condition than their troops.
In many other militaries--particularly those in the third world--you see the exact opposite. In the Honduran military, I witnessed junior enlisted troops who were thin and wiry, while their commanders were habitually obese. The benefits of an officer apparently included sitting around all day and stuffing one's face.
I'd say that General Petraeus isn't setting out to overcompensate for being bookish. I'd say that he, like many generals, is simply out to set a good example. After all, it only says "PASS" on your evaluation.