It is legal to make liquor at home as long as you do not use a still. You might want to check with your state laws because some states limit the percentage of alcohol you can make at home. Each of the Classic Liquors kits will make around 20 - 25% alcohol without the need for a still. This is around the same percentage as most schnapps made. Don’t confuse alcohol percentage with proof. A 20% alcohol liquor is around 40 proof.
The reason why most people can make these kits at home is because they do not require the use of a still. Stills, like the one you saw in M*A*S*H*, are not legal in all 50 U.S. states. Yes, some countries allow using a still for personal use, but the U.S. is not one of them.
What these kits use is a yeast strain capable of reaching higher amounts alcohol without the need for a still. The yeast strain is often called distillers yeast. It's a highly aggressive strain of yeast that can create high percentages of alcohol.
So, unless you happen to live in a state where the percentages are limited, you will be fine to make one of these kits. In about a month, you could be enjoying your own mixed drink.