The DnD-style system is supposed to act as a sort of quick guideline, a set of archetypes that covenants follow. The point isn't to accurately describe the intricate details of the covenant's goals and methods, but to provide an easy way to get the basic idea of covenants to someone brand new to them. This style of presenting things isn't just a DnD thing, it works on a human-psychological level in a way that makes a lot of sense to us and is very familiar. You can generally put any person you know into one of these archetypes.
That doesn't mean it's very accurate. Some fit in their chosen path better than others, and some have aspects that don't fit at all. People shouldn't be using this as a be-all-end-all rule to what these covenants are like, but a precursor to going into the game and finding out for yourself.
One of the problems that lie in the page is that each archetype is filled with a covenant. This means that, unless the designers had such an idea in mind, some covenants get paths that fit them, while other covenants are forced to take what's left over.
The other problem I have is that in the game itself, "Law", "Chaos", "Good", and,"Evil", aren't really clear, nor were they intended to be. Putting covenants in these DnD-style paths makes sense in some environments, such as DnD, where good and evil was mostly clear and predetermined. However, putting them in dark souls sort of forces ideas of what is considered good and evil before the player has a chance to decide that for themselves.
Some things can be made sense of, however. For instance, Lawful and Chaotic can be considered from one's goal, such as following the will of gods and the undead (lawful) or resisting that will. Good and Evil can be considered from the covenant's methods: sacrifice the good of others for your goal, or sacrifice the good of yourself.
With these ideas in mind, the chart fits quite well if you rethink some of the placements, in many cases switching "Lawful/Chaotic" with "Good/Evil". For instance, Princess guard aren't concerned with methods; their goal is to protect Gwynevere (and/or her ideals). Thus, Lawful Neutral fits better than Neutral Good. Gravelord Servent in contrast is not concerned with the will of Gods and Undead. Their methods, however, are brutal and merciless. Thus, Neutral Evil makes more sense than Lawful Evil.
Of course, this still doesn't make this system 100% accurate, but again, that isn't the point. It's supposed to be familiar and make sense to those who are new to the game. It's expected that anybody who plays the game for very long will realize that this system doesn't describe the covenants perfectly. For those people, we have more in-depth pages on each covenant, detailing exactly their ins and outs.