They are definitely counted towards the sugar.
The simple part of the answer is hydration. The primary purpose of the liquid in dough is to hydrate the starch in the flour. Honey and molasses are pure sugars and contain no water. Even though their phase is liquid, they shouldn't be counted as a liquid for making bread. You can't hydrate a starch with sugar.
In fact, the "liquid" part in the bread formula should mean water. There are breads made with liquids other than water (e.g. milk), but these liquids are mostly water with something dissolved in it. A liquid with no water in it doesn't count at all for hydration. This includes honey and oil.
The more complex answer should consider two other effects of liquid in the bread formula. First, there is the dough consistency. Bread is about texture. A liquid dry ingredient will not hydrate the flour, but it will still reduce the viscosity of your dough. Big amounts of it will make a very soft dough which doesn't keep its shape well, has a big oven spring, and in general doesn't behave like classic lean dough. So a recipe containing lots of such an ingredient will still need an adjustment of the amount of hydrating liquid (like water) even though the ingredient (like honey) is considered dry.
The second effect of adding a dry liquid ingredient is that it will make your bread softer. First, you are introducing new molecules into the dough, which keep the gluten strands from finding each other. So you get a less sturdy gluten formation, resulting in a more cakelike bread (yes, cake is cakelike because it has sugar and fat). Also, baked bread loses water over time and gets hard, but sugar binds some of the lost water, and fat prevents the evaporation of the water. A stale enriched (=containing fat and sugar) bread is still stale, but very different in texture from a stale lean bread. So again, you might still want to adjust the amount of hydrating liquid downwards a bit because of this effect your dry ingredient will have on your recipe (or maybe not, if you view the effect as desirable).
Milk is added to bread for flavour, a tender crumb and well-coloured crust.
Dry milk is used because it easy to store and easy to use in bulk. Milk also contains an enzyme called glutathione which can weaken gluten and result in a poorer quality loaf - the drying process destroys this enzyme.
You can substitute regular milk in various proportions, but you may as well simply replace the 2 cups of water with it, which will give you a nice soft loaf. Opinion is divided whether you should scald the milk (by heating to 180°F/82°C according to How Baking Works, page 150) to destroy the glutathione, but in any case it's probably a good idea to warm it anyway, to help the rise.
Best Answer
The taste will change. It will not taste sweet at all, so it wouldn't really be a copy cat recipe any more. It will rise slower. Yeast feeds on sugar, so if you omit the sugar it will only feed on the carbs from the flour and hence rise much slower. And it will likely be less dense. In my experience, adding molasses to a dough makes it denser. It may also become too dry. The molasses especially is a large enough ingredient that omitting it will affect the hydration level of the dough.