The word you've listed here has an L in it, but the word in the book title does not. The book has nothing to do with petrol, but (as one would expect) is a portmanteau of pet and metrosexual. Hence the dogs.
Not sure where the L came in -- it completely changes the word. Petrolsexual doesn't roll off the tongue as well as petrosexual but it's still a nice one; maybe I just like it because petrol is a much better word than gasoline. For what it's worth, I vote for the first definition you suggested. :-)
Another word I excountered last week. A very young girl was sitting in a restaurant, alone, reading a book called "The Complete Petrosexual" while her mom got the pizza. Soon as I got home, I had to find out about the book. Turns out the subtitle is "A Handbook of Style for the Modern Dog." Sigh of relief.
Searched a bit further and found a reference to the word. Source said it was British, a combination of "petrol" and "sexual," modeled on metrosexual. First definition had to a do with a guy whose love object was his car; second definition was a woman who was "hotter than hot"--she is totally petrolsexual! Unfortunately, I've not been able to find the source again.