The tagline plays on the name of the book, "The Missing Manual". . The link you provided states:
Why are there Missing Manuals?
Instead, after paying $300 or more for the software, you're expected to learn these complex programs by reading electronic help screens.
But online help is no substitute for a real manual. Ever try to flip between help topics? Or try to read them over breakfast? Wish you could underline, or at least bookmark what you found? Ah. We thought so.
Software programs don't usually come with manuals, but they come with electronic help. The "Missing Manuals" is help concerning the software programs, and the tagline implies that this Manual should have been in the box, but isn't, so the people who wrote the Manual are providing the Manual(which should have come with the Software Program sold, but isn't) in book form.
The dog is just a play on "missing", which meant that someone (in this case, the dog) has taken the Manual from the boxes of Software Programs, that's why no manuals in Software Program boxes. It's just a playful picture, combining the ideas of "missing" with the dog who tends to take bones (or other stuff, such as shoes) and hiding them.