I think they need to give better explanations. Lets take Lawful Evil for example,
Lawful Evil, “Dominator”: A lawful evil villain methodically takes what he wants within the limits of his code of conduct without regard for whom it hurts. He cares about tradition, loyalty, and order but not about freedom, dignity, or life. He plays by the rules but without mercy or compassion. He is comfortable in a hierarchy and would like to rule, but is willing to serve. He condemns others not according to their actions but according to race, religion, homeland, or social rank. He is loath to break laws or promises.
This reluctance comes partly from his nature and partly because he depends on order to protect himself from those who oppose him on moral grounds. Some lawful evil villains have particular taboos, such as not killing in cold blood (but having underlings do it) or not letting children come to harm (if it can be helped). They imagine that these compunctions put them above unprincipled villains.
Some lawful evil people and creatures commit themselves to evil with a zeal like that of a crusader committed to good. Beyond being willing to hurt others for their own ends, they take pleasure in spreading evil as an end unto itself. They may also see doing evil as part of a duty to an evil deity or master.
Lawful evil is sometimes called “diabolical,” because devils are the epitome of lawful evil.
Lawful evil is the most dangerous alignment because it represents methodical, intentional, and frequently successful evil.
Now think about the show Blackadder, most of the villains and yes the hero, are all Lawful Evil. They either want power, or have it and abuse and manipulate power to the best of their abilities. However, they are more than willing to betray each other, the Crown, and in some cases their own countries for political power. Lets take four characters starting with the Bishop of Bath. The Bishop of Bath is a corrupt, obese, sexually perverted, womanizing, baby eating, mob boss of an Anglican Bishop with a weakness for alcohol in general. Then there's Prince Ludwig, the Indestructible. Prince Ludwig the Indestructible is criminally insane, power hungry, vengeful, methodical, paranoid, and a master of disguise. He even disguised himself as a "very friendly sheep" with which the young Lord Melchart spent a wonderful evening. Then there's Lord Edmund Blackadder II Esquire, he's greedy, intelligent, manipulative, power hungry, and frequently insults people. He derives his personal code from Machivelli. The butler Edmund Blackadder the Third is much like his ancestor Lord Blackadder, except more successful. (Well he does become the Prince Regent, in an episode to convoluted to explain.)
My take on the Evil alignments.
Chaotic Evil. Immoral anarchist. They share the love of freedom but not the respect for life, happiness, or control of one’s own person of other Chaotics. They not only want to destroy all governments, but all society.
Neutral Evil. Willful parasite. They don’t care about power or anarchy, only how much they could suck out of you before you die.
Lawful Evil. Machiavellian. They believe that any action is honorable if it is done in the name of the State. They excuse theft, rape, torture, and murder if it is done in the name of the State. They believe that those who can and will seek power have the moral right to possess it.